Can't go wrong with Sonic and Final Fantasy.

Earthworm jim and Streets of Rage.

Genesis

• Sonic games
• Phantasy Star games
• Shining Force games
• Streets of Rage games
• Vectorman games
• Earthworm Jim games
• Beyond Oasis
• Michael Jackson's Moonwalker
• Castle of Illusion staring Mickey Mouse
• Sword of Vermillion
• Castlevania Bloodlines
• Golden Axe games
• Zombies Ate my Neighbors
• Ghouls 'n Ghosts
• ESWAT

Dreamcast

• Shenmue games
• Rez
• Ikaruga
• Crazy Taxi games
• Grandia 2
• Street Fighter 3 Strike
• Marvel vs Capcom games
• Sega Rally 2
• Metropolis Street Racer
• Record of Lodoss War
• Daytona USA
• Quake 3 Arena
• Rush 2049
• House of the Dead 2
• Virtu Tennis
• D2
• Rayman 2

This is unquestionably the best list.

It mentions Sonic series, Golden axe series and Streets of rage Series for the genesis

And it mentions the best game(s) of all time......... Shenmue 1 & 2 for Dreamcast. (Also jet set radio and metropolis street racer)

For the Genesis i would also reccomend Shinobi 3: Return of the ninja master & Revenge of Shinobi.

Also, if you want some suggestions check out my games list on my profile and get back to me and ask my honest opinion on each game you inquire about.

Well for PS get into Crash bandicoot!!!!

Crash Bandicoot
Crash Bandicoot 2
Crash Bandicoot 3: Warped
Crash Team Racing
Crash Bash

Make sure you get Sonic the Hedgehog 3, and get Sonic and Knuckles. Connect Sonic 3 into the top of the Knuckles cart, and you have the best Sonic experience ever.

Jet Grind Radio, Ikaruga, and Skies of Arcadia for DC.

Dreamcast:

Jet Grind Radio. No matter how many times it's mentioned, it can always be mentioned some more.

I don't think I noticed Bangai-O mentioned anywhere, that game's pretty sweet. I also have a soft spot for Tech Romancer and Cannon Spike. There are loads of good 2D fighting games, such as Last Blade 2, the Vs. series(es), SFIII, Fatal Fury and so on. Tons of shmups, too, if you're into that sort of thing (Gigawing, Mars Matrix, Gunbird). The most insane game ever, Illbleed. Zombie Revenge (boollets!).

And let's not forget the best game of all time, The Typing of the Dead! MWAHAHAHAHA

Oh, I should also mention Sword of the Berserk, Chu Chu Rocket and Space Channel 5 (though the PS2 version of SC5 is better).

EDIT: I also forgot Soul Reaver and Rayman 2.