Arkanoid
Score: 678,540
(Proof)
Balloon Fight
Score: 464,000
2-Player Score (Me & Kevin): 544,500
Jaws
Score: 328,430 (Proof)
Jellyfish Bonus Game: 30/30 (Proof)
Mobile Light Force
Highest Score (without continuing): 756,900 (Difficulty Level 2, using Yuan Nang, 1 death)(Proof)
Doom
I'm not sure if these are good or not, because I've never seen anyone elses, but these are the best I could do. They're from the shareware version.
Hangar: 0:12
Nuclear Plant: 0:37
Toxin Refinery: 0:57
Command Control: 0:37
Phobos Lab: 1:22
Central Processing: 2:15
Computer Station: 2:21
Military Base: 1:47
Games We've No-Deathed
Chico:
Contra
Mike Tyson's Punch-Out (no knockdowns)
Jaws
Super Mario World (no Star Road shortcuts)
Super Monkey Ball (Advanced difficulty + extra stages)
Amplitude (Normal difficulty + bonus songs)
Gradius 3 (Arcade difficulty)
Ikaruga (Normal difficulty/Prototype Mode)
Kevin:
Contra
Astyanax
Gremlins 2
StarFox 64
Gradius
Gradius III (Normal difficulty)
Scramble (through 2 loops)