Also, what's your favorite game for each?
My own list is as follows.
1- Sega Saturn - NiGHTS into Dreams...
The Saturn has to be my favorite game console of all time for one simple reason.
I'm a sucker for the underdog.
Seriously, though. The Saturn is a pretty sweet console. It was the first stand-alone multi-processor game console, the first to have online play capability (with the severely underrated, and STILL FUNCTIONAL, NetLink modem cartridge), and the first with a decent analog controller (the Saturn's optional 3D Control Pad beat the PlayStation's dual analog controller by a few months).
It also had a solid library of arcade titles, as well as several good RPGs and such.
Most original of the bunch, however, has to be NiGHTS into Dreams...
NiGHTS is, bar none, my favorite 3D game of all time. Of ALL time. Incredible to look at, incredible to control, and fun as hell, there hasn't been a more original game in terms of visual style and gameplay since, if you ask me.
And it was only available on Saturn.
2- Sega Genesis - Ranger X.
Ah yes. I don't think anyone can have nothing good to say about this little thing. The Genesis went toe-to-toe with the SNES, and almost won. It's a fun system, cheap to buy used, easy and cheap to collect for. Some of my favorite games of all time were created for this console.
It was also the first real console I ever owned, so it has a very special place in my heart.
My favorite game for it, so far, has to be Ranger X. A prototypical mecha game, it's done in the style of a 2D platform run-n'-gun. It's graphics are incredible, easily the best I've seen on ANY 16-bit console. The gameplay and controls are sublime, and each mission comes with its own unique challenge.
4- Sega Dreamcast - Crazy Taxi.
You can't not love this console. You just can't. It is all things to all gamers.
First of all, even when it first came out, it was cheap. Cheaper than the PS2, certainly.
Second, it was a real nice hunk of hardware. It had the first built-in modem capability, being shipped with a modular 56k modem attachment. It also had powerful graphical processing power, with games that, I think looked as good as anything on the PS2, if not better.
Third, it had a huge library of GREAT games. Everything from platform to racing was represented, and the vast majority of it was VERY good.
In this third category, however, I have to say my favorite title for the system that I've played so far would have to be Crazy Taxi. A great port of the arcade hit, which I've also played, it's a hell of an addicting driving and, to a more limited extent, strategy game. I always find it a relaxing game to play.
Also, it doesn't hurt that it's an almost perfect port from the arcade version. This is mainly due to the fact that Sega's standard arcade hardware at the time was only a Dreamcast with more video RAM.