1. Resident Evil
Remake or Original it doesn't matter. This was a the series that sold me on the PlayStation. I was enthralled playing this game from beginning to end.
2. Mega Man 2
The colorful graphics and music, along with the tight control, made this a game a treat. It was the first platformer after SMB1 that really hooked me on the platform, which was flooded with mediocre entries of that genre.
3. Street Fighter II
I'm giving the original the nod since I spent so much quarters and enjoyed the last years of the arcade scene. This game was everywhere! Laundromats, movie theaters, 7/11. We'll never get another like this culturally.
4. Mega Man X
Much has been written about how genius this game is. I thought the series got diluted in subsequent versions, but this one still remains fresh today.
5. Ghouls and Ghost
I remember the punish prequel, the arcade version, which I saw someone CC to my amazement, and the Genesis version. I still haven't completed a loop of this, but I've always loved the series and this is the best game in it.
6. Duck Tales
I've always been a Disney fan and Capcom's early NES games were a treat. This is the best one. It's basically a sightly different take on Mega Man with new jumping mechanics. One of the best soundtracks of the era as well.
7. Alien Versus Predator
As much as loved Final Fight, Capcom's beat em ups never got better than AvP. The introduction of ranged weapons, SFII style specials, and distinct characters keeps you busy.
8. Demon's Crest
Insanely expensive in the used market, and neglected during it's original release, late in the SNES lifecycle. DC was darker than the previous Gargoyle games, but offered much more options and huge levels. There is some backtracking a la Metroid, but ti's done well.
9. DMC3
While DMC4 has the best combat, the lack of environmental variety and enemies hurt it. DMC3 was a huge step forward in the series, refining its battle system, and upping the difficulty.
10. Dead Rising
The game that sold me on the 360. Lightweight reviewers complained about the punishing save system and time limit, but it was perfect. I never connected to most open world games, but the mall in DR was a fun place to explore.