My 15 all undrafted and in no particular order...
1. WWF No Mercy (N64)
2. Fire Pro Wrestling S: 6 Men Scramble (Sega Saturn)
Far and away my two favorite wrestling games. No Mercy had a pick up and play ability that I could be playing these games year round and bring it home for Thanksgiving and Christmas and my brother could jump in and we'd have great games. Nobody did customization in this era like Fire Pro and frankly the grapple system was maybe outside of the AKI engine's extreme ease of pick up and play, the best alternative. Honorable mentions to NES Pro Wrestling and Mat Mania
3. NFL 2K5 (Dreamcast)
Broke the Madden grip, probably best football simcade game ever made. All Pro 2k8 is also super fun but I am going with the one with the license. EA got so upset they bought exclusive rights to NFL, NCAA
AND the Arena Football League to freeze 2k out.
4. Rock Band 3 (Xbox 360)
Pinnacle of the series for me. Pro mode with effectively real drums and guitar. Keyboards. Three part vocal harmonies. Rock Band Network. Pretty sure it also had the best career mode and character creator suite. Rock Band 4 kept alive for the next/current gen but dropped all that cool stuff and went back to basics.
5. NHL 2K3 (Xbox)
If I recall correctly this was the first hockey game with Xbox Live support. Descended from Power Play Hockey (amazing) the 2K series was far more sim like and topped EA for years until the mid-00s. This one I give the nod for being my first online NHL experience.
6. Deathrow (Xbox)
As a die hard sports gamer I also had a love for future-sports games - this one may have been the best of the best.
7. The Pinball Arcade (iOS)
No pinballs were taken. I am not sure if that was a strict rule or not, but being a digital game this one gets a pass. I pick the iOS version because it can be played with vertical orientation. Sadly they lost the Williams pinball license in 2018 but presumably since if you bought them you keep them, I'd have all of those too.
8. Skate 3 (Xbox 360)
THPS 2 and 4 are my favorites of that series but Skate really upped the ante with the trick sticks and realism. Hard time picking which one but I do think Skate 3 is the most feature packed. The lack of features actually made some of the OG Skate pretty cool though - just hitting some huge insane gaps and having to actually stick a clean landing. So awesome.
9. College Hoops 2K8 (Xbox 360)
College sports games are so fun. 2K8 was insane and the last of the series. So much fun recruiting your class. Way more fun for a great basketball playing game with stuff to do on the side than the trading card games NBA 2k MyTeam has become. Sega actually made a pretty killer College Football title on Genesis as part of the Sports Talk line. I had to mention here or in the 2K football, because those games were pretty killer and worthy of play in the early Madden days as well.
10. DecAthlete (Sega Saturn)
Did the olds playing along ever play Decathlon on 2600? I loved that game and chasing records but the joystick wiggling mechanic is no bueno. This was another Decathlon arcade game released on Saturn around the Atlanta Games. We used to have the best time at my condo in Boston playing this one with 4 of us chasing our own records. Another pick up and play party game that was super fun before online ruled everything.
Honorable mention in this category to Epyx for Summer Games, Winter Games, California Games, and The Games: Winter Edition
11. Police Quest (Apple ][ GS)
Leisure Suit Larry was picked and I loved all these Sierra games. In the late 80s they were up there with EA for me. This is the earlier version of the game that had the text interface and not the later one where you could mouse click to solve everything. Such a fun one. All the Quest games were awesome in their own right and I sorta feel guilty for picking the cop one instead of a Space Quest or something but what the heck.
12. Red Baron (PC)
Hard time choosing between Dynamix flight sims. I think that Aces of the Pacific was my favorite, but Red Baron could be played online through the Imagination Network in the early through mid-90s and was so much fun. Probably the most fun I would have on a dial up modem. I loved aerial combat games, from X-Wing and Tie Fighter to these. Especially when you could turn off enough simulation to make them fun but leave on enough that it wasn't just an arcade game.
13. Crimson Skies: High Road to Revenge (Xbox)
Developed by FASA (of MechWarrior/Mech Assault fame) this one was another aerial combat game on Xbox Live for the OG Xbox. It was an absolute blast, kind of a retro future story. Fun online modes.
Honorable mention in the dog fight game category to Wings of Fury on the Apple ][. This was a killer 80s dogfight side scroller. So much fun, I'd have Iron Maiden's Aces High playing constantly.
14. Fallout 2 (PC)
The first two Fallouts were my favorite. Don't blame
@hrdboild for taking the original but F2 was infinitely bigger. If this is some desert island thing, I'll take the extra options. Ok, confession time: I never beat it. I beat the first. So that's also why.
15. Star Wars Knights of the Old Republic (Xbox)
I really don't understand how this one did not get picked. Classic BioWare RPG with an awesome Star Wars story. The one Star Wars game I'd put up against Tie Fighter.
I probably have another 5-10 honorable mentions. Sandbox: Mercenaries. FPS: Outlaws. Turnbased Strategy: Jagged Alliance. Classic action/RPG: AutoDuel and Mobius. Karateka... oh man.
Like I said, I played a crap ton of games since my dad brought home the VCS up until when I got divorced and my time got busy with all my other responsibilities.