Here are my best times in Sonic Adventure 2 Battle, Sonic Heroes and Sonic Rush. Some of these are easy to beat, and some of them are difficult.

Sonic Adventure 2 Battle:
I've done all these times in the fouth mission without any checkpoints.

Sonic's stages:

City Escape: 02:02:69
Metal Harbor: 01:30:99
Green Forest: 02:00:45
Pyramid Cave: 02:30:94
Crazy Gadget: 03:24:87
Final Rush: 03:12:27
Green Hill: 00:36:95

Shadow's stages:

Radical Highway: 02:05:09
White Jungle: 02:04:34
Sky Rail: 00:56:52
Final Chase: 03:57:72

Sonic Heroes:
These times were done with sonic team. Some of these times are easy, because this game doesn't have many shortcuts, but most of these are still hard to beat.

Seaside Hill: 03:34:53
Ocean Palace: 03:33:68
Grand Metropolis: 03:20:61
Power Plant: 06:11:53
Casino Park: 03:02:86
Bingo Highway: 05:41:24
Rail Canyon: 03:56:04
Bullet Station: 05:33:38
Frog Forest: 03:19:36
Lost Jungle: 04:31:29
Hang Castle: 05:46:71
Mystic Mansion: 06:22:06
Egg Fleet: 05:44:31
Final Fortress: 08:35:19

Sonic Rush:
These times are almost impossible to beat even for me (OMG!).

Zone 1: Leaf Storm
act1: 0:46:96
act2: 1:09:01

Zone 2: Water Palace
act1: 1:04:43
act2: 1:18:89

Zone 3: Mirage Road
act1: 2:35:55
act2: 2:55:20

Zone 4: Night Carnival
act1: 1:30:52
act2: 2:31:43

Zone 5: Huge Crisis
act1: 1:53:84
act2: 2:12:77

Zone 6: Altitude Limit
act1: 2:45:62
act2: 2:48:79

Zone 7: Dead Line
act1: 2:17:52
act2: 2:33:05

Zone X
act1: 0:47:59
act2: 0:52:35
act3: 1:15:13
act4: 1:34:10

Sonic Riders:

I did these times in time attack-mode.

Best Times:

Metal City: 02:04:18
Splash Canyon: 02:14:18
Egg Factory: 02:21:48
Green Cave: 02:28:80
Sand Ruins: 02:41:28
Babylon Garden: 02:58:98
Digital Dimension: 02:52:54
Sega Carnival: 02:33:32
Night Chase: 02:08:58
Red Canyon: 02:35:28
Ice Factory: 02:59:72
White Cave: 02:17:18
Dark Desert: 02:37:54
Sky Road: 02:13:72
Babylon Guardian: 01:39:48
Sega Illusion 02:50:92

Best Laps:

Metal City: 00:39:18
Splash Canyon: 00:43:30
Egg Factory: 00:45:74
Green Cave: 00:48:94
Sand Ruins: 00:53:62
Babylon Garden: 00:55:84
Digital Dimension: 00:55:64
Sega Carnival: 00:48:52
Night Chase: 00:40:34
Red Canyon: 00:51:28
Ice Factory: 00:58:46
White Cave: 00:44:42
Dark Desert: 00:49:34
Sky Road: 00:39:48
Babylon Guardian: 00:32:88
Sega Illusion 00:55:78

Have fun trying to beat these!