To unlock the mini-games, you simply have to start the various normal games a certain number of times:

Flicky mini-game:
Enter Dr. Robotnik's Mean Bean Machine 50 times.

Blue Spheres mini-game:
Enter Sonic the Hedgehog and Sonic 3D Blast 20 times each.

Play Knuckles in Sonic 2:
Enter Sonic Spinball and Sonic 2 50 times each.

Blue Spheres Level Select:

Level	Password
1	3659 8960 3263
2	2965 3192 9023
3	3610 2354 7327
4	2921 0274 3999
5	3737 7423 1487
6	3053 9029 9071
7	3698 8191 7375
8	3009 6111 4047
9	3482 7286 3167
10	2809 6267 2575
11	3454 5929 0879
12	2765 3348 7551
13	3582 0497 5039
14	2898 2104 2623
15	3543 1266 0927
16	2853 9185 7599
17	4014 2308 3455
18	3319 6540 9215
19	3964 5702 7519
20	3275 3622 4919
21	4092 0771 1679
22	3408 2377 9263
23	4053 1539 7567
24	3363 9449 4239
25	3837 0634 3359
26	3163 9615 2764
27	3808 8777 1068
28	3119 6696 7740
29	3936 3845 5228
30	3252 5452 2812
31	3897 4614 1116
32	3208 2533 7788
33	2994 5155 4236
34	3673 9888 9404
35	2944 5155 4236
36	3629 6970 4380
37	3072 0223 8396
38	3762 5728 9452
39	3033 0992 4284
40	3718 2807 4428
41	2817 0087 0076
42	3518 2963 2956
43	2788 8229 7788
44	3474 0044 7932
45	2916 3298 1948
46	3606 8800 3004
47	2877 4066 7836
48	3562 5881 7480
49	3348 5109 0364
50	4028 3236 9596
51	3298 8503 4428
52	3984 0318 4572
53	3426 3571 8588
54	4116 9073 9644
55	3387 4340 4476
56	4072 6155 4620
57	3171 3435 0268
58	3829 6814 5852
59	3100 2081 0684
60	3785 3896 0828
61	3227 7149 4844
62	3918 2651 5900
63	3188 7918 0732
64	3873 9733 0876
65	5034 2855 6732
66	4339 7088 2492
67	4984 6250 0796
68	4295 4169 7468
69	5112 1318 4956
70	4428 2925 2540
71	5073 2087 0844
72	4384 0006 7516
73	4857 1181 6636
74	4184 0162 6044
75	4828 9324 4348
76	4139 7244 1020
77	4956 4392 8508
78	4272 5999 6092
79	4917 5161 4396
80	4228 3081 1068
81	5388 6203 6924
82	4694 0436 2684
83	5338 9598 0988
84	4649 7517 7660
85	5466 4666 5148
86	4782 6273 2732
87	5427 5435 1036
88	4738 3354 7708
89	5211 4529 6828
90	4538 3510 6237
91	5183 2672 4541
92	4494 0592 1213
93	5310 7740 8701
94	4626 9347 6285
95	5271 8509 4589
96	4582 6429 1261
97	4368 5656 3645
98	5048 3784 2877
99	4318 9050 7709
100	5004 0865 7853
101	4446 4119 1869
102	5136 9621 2925
103	4407 4887 7757
104	5092 6702 7901
105	4191 3982 3549
106	4892 6858 6429
107	4163 6858 6429
108	4848 3940 1405
109	4290 7193 5421
110	4981 2695 6477
111	4251 7962 1309
112	4936 9777 1453
113	4722 9004 3837
114	5402 7132 3069
115	4673 2398 7901
116	5358 4213 8045
117	4800 4767 2061
118	5491 2969 3117
119	4761 8235 7949
120	5447 0050 8093
121	4545 7330 3741
122	5204 0709 9325
123	4474 5976 4157
124	5159 7791 4301
125	4602 1044 8317
126	5292 6546 9373
127	4563 1813 4205
128	5248 3628 4349
129	3659 8750 6109
130	2965 2983 1869
131	3610 2145 0173
132	2921 0064 6845
133	3737 7213 4333
134	3053 8820 1917
135	3698 7982 0221
136	3009 5901 6893
137	3482 7076 2809
140	2765 3139 0397
141	3582 0287 7885
142	2898 1894 4569
143	3543 1056 3773
145	4014 2098 6301
144	2853 8976 0445
146	3319 6331 2061
147	3964 5493 0365
148	3275 3412 7037
149	4092 0561 4525
150	3408 2168 2109
151	4053 1330 0413
152	3363 9249 7085
153	3837 0424 6205
154	3163 9405 5602
155	3808 8567 3906
156	3119 6487 0578
157	3936 3635 8066
158	3252 5242 5650
159	3897 4404 3954
160	3208 2324 0626
161	2994 1551 3010
162	3673 9679 2242
163	2944 4945 7074
164	3629 6760 7218
165	3072 0014 1234
166	3762 5516 2290
167	3033 0782 7122
168	3718 2597 7266
169	2816 9877 2914
170	3518 2753 5794
171	2788 8020 0626
172	3473 9835 0770
173	2916 3088 4766
174	3606 8590 5842
175	2877 3857 0674
176	3562 5672 0818
177	3348 4899 3202
178	4028 3027 2434
179	3298 8293 7266
180	3984 0108 7410
181	3426 3362 1426
182	4116 8864 2482
183	3387 4130 7314
184	4072 5945 7458
185	3171 3225 3106
186	3829 6604 8690
187	3100 1871 5322
188	3785 6939 7682
189	3227 6939 7682
190	3918 2441 8738
191	3188 7708 3570
192	3873 9523 3714
193	5034 2645 9570
194	4339 6878 5330
195	4984 6040 3634
196	4295 3960 3634
197	5112 1108 7794
198	4428 2715 5378
199	5073 1877 3682
200	4383 9797 0354
201	4828 0971 7186
202	4183 9952 8882
203	4828 9114 7186
204	4139 7034 3858
205	4956 4183 1346
206	4272 5789 8930
207	4917 4951 7234
208	4228 2871 3906
209	5388 5993 5762
210	4694 0226 5522
211	5338 9388 3826
212	4649 7308 1498
213	5466 4456 7986
214	4782 6063 5570
215	5427 5225 3874
216	4736 3145 0456
217	5211 4319 9666
218	4538 3300 9075
219	5183 2462 7379
220	4494 0382 4051
221	5310 7531 1539
222	4642 9137 9123
223	5271 8299 7427
224	4582 6219 4099
225	4368 5446 6483
226	5048 3574 5715
227	4318 8841 0547
228	5004 0656 0691
229	4446 3909 4707
230	5136 9411 5763
231	4407 4678 0595
232	5092 6493 0739
233	4191 3772 6348
234	4892 6648 9267
235	4163 1915 4099
236	4848 3730 4243
237	4290 6983 8259
238	4981 2485 9315
239	4251 7752 4147
240	4936 9567 4291
241	4722 8794 6675
242	5402 6922 5907
243	4673 2189 0739
244	5358 4004 0883
245	4800 7257 4899
246	5491 2759 5955
247	4761 8026 0787
248	5446 9841 0931
249	4545 7120 6579
250	5204 0500 2163
251	4474 5766 6995
252	5159 7581 7139
253	4602 0853 1155
254	5292 6337 2211
255	4563 1603 7043
256	5248 3418 7187
257	3659 3979 7555
258	2965 3612 3315
259	3610 2774 1619
260	2921 0693 8291
261	3737 7842 5779
262	3053 9449 3363
263	3698 8611 1667
264	3009 6530 8339
265	3482 7705 7459
266	2809 6686 6867
267	3454 5848 5171
268	2765 3768 1843
269	3582 0916 9331
270	2898 2523 6915
271	3543 1685 5219
272	2853 9605 1891
273	4014 2727 7747
274	3319 6960 3507
275	3964 6122 1811
276	3275 4041 8483
277	4092 1190 5971
278	3408 2797 3555
279	4053 1959 1859
280	3363 9878 8531
281	3837 1053 7651
282	3164 0034 7056
283	3808 9196 5360
284	3119 7116 2032
285	3936 4264 9520
286	3252 5871 7104
287	3897 5033 5408
288	3208 2953 2080
289	2994 2180 4464
290	3674 0308 3696
291	2944 5574 8582
292	3629 7389 9672
293	3072 0643 2688
294	3762 6145 3744
295	3033 1411 8576
296	3718 3326 8720
297	2817 0506 4368
298	3518 3382 7248
299	2788 8649 2080
300	3474 0464 2224
301	2916 3717 6240
302	3606 9219 7296
303	2877 4486 2128
304	3562 6301 2272
305	3348 5528 4656
306	4028 3656 3888
307	3298 8922 8720
308	3984 0737 8864
309	3426 3991 2880
310	4116 9493 3936
311	3387 4759 8768
312	4072 6574 8912
313	3171 3854 4560
314	3829 7234 0144
315	3700 2500 4976
316	3785 4315 5120
317	3227 7568 9136
318	3918 3071 0192
319	3188 8337 5024
320	3874 0152 5168
321	5034 3275 1024
322	4339 7507 6784
323	4984 6669 5088
324	4295 4589 1760
325	5112 1737 9248
326	4428 3344 6832
327	5073 2506 5136
328	4384 0426 1808
329	4857 1601 0928
330	4184 0582 0336
331	4828 9743 8640
332	7139 7663 5312
333	4956 4812 2800
334	4272 6419 0384
335	4917 5580 8688
336	4228 3500 5360
337	5388 6623 1216
338	4694 0855 6976
339	5339 0017 5280
340	4649 7937 1952
341	5466 5085 9440
342	4782 6692 7024
343	5427 5854 5328
344	4738 3774 2000
345	5211 4949 1120
346	4538 3930 0529
347	5138 3091 8833
348	4494 1011 5505
349	5310 8160 2993
350	4626 9767 0577
351	5271 8928 8881
352	4582 6848 5553
353	4368 6075 7937
354	5048 4203 7169
353	4318 9470 2001
356	5004 1285 2145
357	4446 4538 6161
358	5137 0040 7217
359	4407 5307 2049
360	5092 7122 2193
361	4191 4401 7841
362	4892 7278 0721
363	4163 2544 5553
364	4848 4359 5697
365	4290 7612 9713
366	4981 3115 0769
367	4251 8381 5601
368	4937 0196 5745
369	4722 9423 8129
370	5402 7551 7361
371	4673 2818 2193
372	5358 4633 2337
373	4800 7886 6353
374	5491 3388 7409
375	4761 8655 2241
376	5447 0470 2385
377	4545 7749 8033
378	5204 1129 3617
379	4474 6395 8449
380	5159 8210 8593
381	4602 1464 2609
382	5292 6696 3665
383	4563 2232 8497
384	5248 4047 8641
385	3659 9170 0401
386	2965 3402 6161
387	3610 2564 4465
388	2921 0484 1137
389	3737 7632 8625
390	3053 9239 6209
391	3698 8401 4513
392	3009 6321 1185
393	3482 7496 0305
394	2809 6476 9713
395	3454 5638 8017
396	2765 3558 4689
397	3582 0707 2177
398	2898 2313 9761
399	3543 1475 8065
400	2853 9395 4737
401	4014 2518 0593
402	3319 6750 6353
403	3964 5912 4657
404	3275 3832 1329
405	4092 0980 8817
406	3408 2587 6401
407	4053 1749 4705
408	3363 9669 1377
409	3837 0844 0497
410	3163 9824 9910
411	3808 8986 8214
412	3119 6906 4886
413	3936 4055 2374
414	3252 5661 9958
415	3897 4823 8262
416	3208 2743 4934
417	2994 1970 7318
418	3674 0098 6550
419	2944 5365 1382
420	3629 7180 1526
421	3072 0433 5542
422	3762 5935 6598
423	3033 1202 1430
424	3718 3017 1574
425	2817 0296 7222
426	3518 3173 0102
427	2788 8439 4934
428	3474 0254 5078
429	2916 3507 9094
430	3606 9010 0150
431	2877 4276 4982
432	3562 6091 5126
433	3348 5318 7510
434	4028 3446 6742
435	3298 8713 1574
436	3984 0528 1718
437	3426 3781 5734
438	4116 9283 6790
439	3387 4550 1622
440	4072 6365 1766
441	3171 3644 7414
442	3829 7024 2998
443	3100 2290 7830
444	3785 4105 7974
445	3227 7359 1990
446	3918 2861 3046
447	3188 8127 7878
448	3873 9942 8022
449	5034 3065 3878
450	4339 7297 9638
451	4984 6459 7942
452	4295 4379 4614
453	5112 1528 2102
454	4428 3134 9686
455	5073 2296 7990
456	4384 0216 4662
457	4857 1391 3782
458	4184 0372 3190
459	4828 9534 1494
460	4139 7453 8166
461	4956 4602 5654
462	4272 6209 3238
463	4917 5371 1542
464	4228 3290 8214
465	5388 6413 4070
466	4694 0645 9830
467	5338 9807 8134
468	4649 7727 4806
469	5466 4876 2294
470	4782 6482 9878
471	5427 5644 8182
472	4738 3564 4854
473	5211 4739 3974
474	4538 3720 3383
475	5183 2882 1687
476	4494 0801 8359
477	5310 7950 5847
478	4626 9557 3431
479	5271 8719 1735
480	4582 6638 8407
481	4368 5866 0791
482	5048 3994 0023
483	4318 9260 4855
484	5004 1075 4999
485	4446 4328 9015
486	5136 9831 0071
487	4407 5097 4903
488	5092 6912 5047
489	4191 4192 0695
490	4892 7068 3575
491	4163 2334 8407
492	4848 4149 8551
493	4290 7403 2567
494	4981 2905 3623
495	4251 8171 8455
496	4936 9986 8599
497	4722 9214 0983
498	5402 7342 0215
499	4673 2608 5047
500	5358 4423 5191

Dr. Robotnik's Mean Bean Machine Level Select:

Difficulty Level	Opponent	Password
Easy
2	Frankly	Red, Red, Red, Has Bean
3	Humpty	Clear Bean, Purple, Clear Bean, Green
4	Coconuts	Red, Clear Bean, Has Bean, Yellow
5	Davy Sproket	Clear Bean, Blue, Blue, Purple
6	Sqweel	Clear Bean, Red, Clear Bean, Purple
7	Dynamight	Purple, Yellow, Red, Blue
8	Grounder	Yellow, Green, Has Bean, Blue
9	Spike	Yellow, Purple, Has Bean, Blue
10	Sir Fuzzy Logik	Red, Yellow, Clear Bean, Has Bean,
11	Dragon Breath	Green, Purple, Blue, Clear Bean,
12	Scratch	Red, Has Bean, Has Bean, Yellow,
13	Dr. Robotnik	Yellow, Has Bean, Blue, Blue
Normal
2	Frankly	Has Bean, Clear Bean, Yellow, Yellow
3	Humpty	Blue, Clear Bean, Red, Yellow
4	Coconuts	Yellow, Blue, Clear Bean, Purple
5	Davy Sproket	Has Bean, Green, Blue, Yellow
6	Sqweel	Green, Purple, Purple, Yellow
7	Dynamight	Purple, Blue, Green, Has Bean
8	Grounder	Green, Has Bean, Clear Bean, Yellow
9	Spike	Blue Purple, Has Bean, Has Bean
10	Sir Fuzzy Logik	Has Bean, Red, Yellow, Clear Bean
11	Dragon Breath	Clear Bean, Red, Red, Blue
12	Scratch	Green, Green, Clear Bean, Yellow
13	Dr. Robotnik	Purple, Yellow, Has Bean, Clear Bean
Hard
2	Frankly	Green, Clear Bean, Yellow, Yellow
3	Humpty	Yellow, Clear Bean, Purple, Clear Bean
4	Coconuts	Blue, Green, Clear Bean, Blue
5	Davy Sproket	Red, Purple, Green, Green
6	Sqweel	Yellow, Yellow, Clear Bean, Green
7	Dynamight	Purple, Clear Bean, Blue, Blue
8	Grounder	Clear Bean, Yellow, Has Bean, Yellow
9	Spike	Purple, Blue, Blue, Green
10	Sir Fuzzy Logik	Clear Bean, Green, Red, Yellow
11	Dragon Breath	Blue, Yellow, Yellow, Has Bean
12	Scratch	Green, Clear Bean, Clear Bean, Blue
13	Dr. Robotnik	Has Bean, Clear, Purple, Has Bean
Hardest
2	Frankly	Blue, Blue, Green, Yellow
3	Humpty	Green, Yellow, Green, Clear Bean
4	Coconuts	Purple, Purple, Red, Has Bean
5	Davy Sproket	Green, Red, Purple, Blue
6	Sqweel	Blue, Purple, Green, Yellow
7	Dynamight	Blue, Purple, Green, Has Bean
8	Grounder	Clear Bean, Purple, Has Bean, Yellow
9	Spike	Purple, Green, Has Bean, Clear Bean
10	Sir Fuzzy Logik	Green, Blue, Yellow, Has Bean
11	Dragon Breath	Green, Purple, Has Bean, Red
12	Scratch	Red, Green, Has Bean, Blue
13	Dr. Robotnik	Red, Red, Clear Bean, Yellow

Sonic The Hedgehog - Cheat mode:
At the Sonic The Hedgehog title screen, press Up, Down, Left, Right. Hold B for level select and sound test.

Sonic The Hedgehog - Debug mode:
At the Sonic The Hedgehog title screen, press Up, X, Down, X, Left, X, Right, Up, X, Down, X, Left, X, Right, X, Now hold B and press Start. Press A to enter debug mode.

Sonic The Hedgehog 2 - Level select:
Go to Sound Test option. Choose sounds 19, 65, 9, and 17. Hold X and press Start to return to the title screen, then hold B and press Start to access the level select menu.

Sonic The Hedgehog 2 - Super Sonic:
Enable the "Level select" code and go to Sound Test option. Choose sounds 4, 1, 2, 6. Start a stage, collect 50 rings, then jump to transform into Super Sonic.

Sonic The Hedgehog 2 - Debug mode:
Enable the "Level select" code and go to Sound Test option. Choose sounds 1, 9, 9, 2, 1, 1, 2, 4. Select any starting level, then hold B + Start until play begins. Screen coordinates will appear instead of a score and the number of objects displayed will appear instead of the time remaining. To edit the level, press the button configured as B on the Genesis. Sonic should become an object somewhere on the level. Press the button configured as C to "paste" that object in the level. Press the button configured as B again to resume game play.

Sonic and Knuckles - Level select:
Start a game with Sonic and run over to the Madmole near the Super Shoes power-up. Directly to the right of the Madmole is a pulley mechanism that takes you to the next level above by pushing Down on it. Instead of pushing down, push the Left, Left, Left, Right, Right, Right, Up, Up, Up. Now press Start to pause the game and press B. You will be sent back to the main screen. When you can select between Sonic and Knuckles, hold B and press Start for a level select.

Sonic The Hedgehog 2 And Knuckles - Level select:
At the Sonic The Hedgehog 2 title screen, press Up, Up, Up, Down, Down, Down, Left, Right, Left, Right, press and hold B, and then press Start. A stage select screen will appear.

Sonic Spinball - Level select:
At the Main Menu, select Options. Now at the Options screen, press A, Down, B, Down, X, Down, A, B, Up, A, X, Up, B, X, Up. You should hear a sound to confirm. Return to the main menu and then enter the following codes to unlock the corresponding level.

Level 2: Hold A and press Start
Level 3: Hold B and press Start
Level 4: Hold X and press Start

Sonic 3D Blast - Level Select:
When "Press Start" appears on the Sonic 3D Blast title screen, press B, A, Right, A, X, Up, Down, A, Start.

Unlock Flicky Bonus Game:
Insert a memory card with a save file for Sonic Adventure 2 Battle, and Flicky will be available at the Games menu.