Go big or go home!
Nintendo
The best little retro system out there. Besides the great shmups, platformers, and Nintendo staples, it also had the best versions of the old arcade games. If I had to keep only one console and get rid of the rest, I would keep the NES without a doubt.
Super Nintendo
To me, the SNES is just the NES but polished with the introduction of RPGs. Generally, it only really lacks the plethora of 8-bit arcade games that really makes the NES shine, but where the NES was the beginning (Contra, Metroid, Zelda, Mega Man, Final Fantasy, Donkey Kong, Gradius) the SNES was the peak. Very close, but not quite a tie.
Genesis
The Genesis was my first console that was mine, and it will always have a special place in my heart. Despite that, I felt that overall the games were just better on the SNES. Looked better, sounded better, controlled better (except where the same game was on both), and it lacked the many excellent RPGs the SNES had. Platformers and shmups, two of my favorite genres, are where it really shines, so it definitely ranks way up there.
PlayStation
Saturn
These two are almost a tie, and they both are excellent 32 bit systems, It's a close call which one is better, since for most 2D games I'd rather have it on the Saturn, find them superior on the Saturn, but I give the slight edge to the PS for having more and better RPGs and for just having more games in general. It's a close call, though, since for most 2D games I'd rather have it on the Saturn, find them superior on the Saturn.
PlayStation 2
PS2 ranks so high for me merely because of what it offers. There is just so much in the library, that it's easy to amass a huge collection of quality games. Only problem is, very few of them I think rank among the best of the pre-DC era. Racing games are the one exception. Of its peers, though, it's the best.
7800
If you have a 7800 that can play all 2600 games, what's the point of having a 2600? And having all 2600 games is the only reason the 7800 is up so high. Without backwards compatibility, the 7800 would rank much lower to me, but the two libraries combined make a formidable experience in early arcade-style games. It also has the best port of Centipede, and that alone makes it worth owning. The homebrew scene has also done it nicely.
Nintendo 64
The N64 is the king of party consoles. Mario Kart 64 and Ogre Battle 64 alone are worth it, but Puyo Puyo, Bust-a-Move, GoldenEye/Perfect Dark, etc. make it a pleasure to play with all types of folks. That and that alone is why it ranks higher than the Dreamcast.
Dreamcast
HOMEBREW! HOMEBREW! HOMEBREW! Yes, I love my DC for the arcade style games it offers, not shit like Shenmue, and for the excellent homebrew and great shmups and 2D fighters it offers.
GameCube
The GameCube is an underrated gem. It's got a lot of great non-Nintendo stuff on it. While the 1st party stuff is great, it has just enough of each genre and really shines at what it does have. Add the ability to play Game Boy Advance games and you have a most impressive system.
Master System
I like the Master System plenty, but I feel it couldn't really compete with the NES. It holds its own, but with a few of its older arcade conversions mitigated by later releases (like R-Type), it suffers. I'm still exploring this library, so it may surpass the GameCube, but I doubt I'll surpass the DC for me.
Wii
The Wii is all right. Online multiplayer is OK, the games are not bad. Since I don't have a 360 or PS3, it also acts as a Netflix device. Nothing special, and I don't care for motion controls.
Xbox
The Xbox is cool and doesn't afraid of anything.
Neo Geo CD
I hope I don't get too much hate for this, but ugh, ugh, ugh load times are a bitch.
ColecoVision
Ah, the Colecovision. I don't mean to hate on it, and I'm not, I swear! But I'm not as familiar with its overall library, so it can't rank too high. A solid console that makes a better version of several 2600 games, which alone make it worth owning.
Handhelds:
Game Boy
The system itself is balls, but the games alone do it for me.
Neo Geo Pocket Color
Despite the paltry library, it has the best stick of all time. OF ALL TIME!
Game Boy Color
This should have had a backlight. That bums me out. But still, plenty of excellent games, and builds solidly on the Game Boy library.
DS
Truth be told, I'm not enamored with the post-GBC Nintendo handhelds, but there are some real gems among them. I think the DS beats out the GBA but just barely. I think the more I explore it, the better it gets, so that's something.
Game Boy Advance/SP
Gotta have a backlight. SP AGS-101. The library is only OK. So many of these games I find to be not as fun. Adventure games are just gimped adventures. There is some fun to be had, though.
Game Gear
The Game Gear has too few exclusives to make it a good handheld. It was great in the old days, though, before I got a Master System.