The Next Tetris (PS1)
This game is very mediocre. The meat and potatoes of it is a new mode that involves blocks that have different colors on them that fall separately from the blocks. For example, a T block could have a yellow block on one side that'll fall independently of the rest of the red blocks. The music is incredibly quiet and lame, but as a plus the whole game loads to RAM when you start it, so you can take the disc out and play your own CD of music. Overall this one is boring.
Tetris (Game Boy)
What can I say about this one? You've all played it. Very solid Tetris game. Also very barebones.
Tetris Axis (3DS)
A very fun Tetris with a ton of modes that got poor reviews for some reason. Yeah, it's no Tetris DS, but it's still just as fast-paced and fun, and has Bombliss mode, one of my favorites, which is an implementation of Tetris Blast.
Tetris & Dr. Mario (SNES)
Another barebones Tetris, with Dr. Mario bundled alongside it. The music is nice and it has a neat multiplayer mode called Mix & Match where you play a round of Tetris and a round of Dr. Mario.
Tetris 2 (Game Boy)
This one's weird. It's not a traditional Tetris game. The blocks are different colors and you match them up like Dr. Mario instead of clearing lines. I honestly don't like it very much, but it's a neat twist on the formula.
Tetris Attack (Game Boy)
Technically not a Tetris game at all. It involves matching up blocks that rise up from the bottom in a match-3 sort of game. A good stress reliever, until you get to the higher levels.
Tetris Blast (Game Boy)
This is another non-traditional Tetris which shows up every now and then as a side mode in Tetris games. Instead of clearing blocks by making lines, there are blocks which have a bomb inside them. If you make a line with a bomb in it, the bombs explode in chain reactions. It's a really good game with some awesome music.
Tetris DS (DS)
This is hands down the best Tetris game ever made. Lots of unique modes, and it's Nintendo themed with awesome remixes of classic Nintendo tunes. It's a fast paced modern Tetris with hard drop, 5 next pieces and infinite spin, so if you're one of those people who are so stuck in nostalgialand that you can't play anything that's not the classic you should stay far, far away.
Tetris DX (Game Boy Color)
Take the original GB Tetris and add some color and change the music. That's basically all this is. Nothing really special about it beyond the added Ultra and 40 Lines modes.
Tetris Plus (PS1)
Jaleco's take on Tetris. This one's pretty standard fare with an added puzzle mode (with a level editor!) where you're helping an explorer escape a temple by giving him a staircase of blocks to climb. It has a cute anime theme to it.
Tetris Plus (Game Boy)
This is a watered down version of the PS1 game. It's essentially the same, minus the color and CD quality music. Even the level editor is intact!
Tetris Ultimate (3DS)
Do not buy this Tetris! It only has one mode at first, and you have to unlock the other ones later. Only one song and it's kind of haunting and not fun, like a Tetris song should be. It's just full of "wrongness".
Tetris Worlds (PS2/Xbox/GameCube)
The Tetris that solidified the modern Tetris formula. The theme is kind of... odd. I don't dislike this one, but it's not a go-to for me by any means. It has hard drop and hold all of that, but the pieces aren't segmented, they're smooth, so it's kind of disorienting to play.
Tetris Worlds (GBA)
A watered down Tetris Worlds for GBA. A lot of the modes are stripped, so you're left with a pretty barebones Tetris. Nothing wrong with it, nothing stand-out about it.
Tetris: The Card Game (Card Game)
I can't honestly review this one because I never took it out of the box. But it looks really interesting!
What Tetris games that I didn't mention do you like?