Kind of a "reverse Tetris puzzle/shmup hybrid", where you shot blocks to fill the lines that descend from the top. Your objective is to fill the lines to create quadrilaterals, which then disappear.
Classic puzzle, you must shift the colors of the columns dropping from the top of the screen to stack jewels and form lines of three or more of the same color to make them disappear. Has ports on practically every Sega console.
You control a paddle, and must catch the colored tiles that slide down the ramp to stack them. Don't let the tiles fall down the pit!
Magical Drop III
Another classic, drag and drop the colored drops, match them and create chains to mess up your adversary. Play the Japanese version, they butchered the game in the international versions.
You can play the early games, but the AI is all sorts of bullshit. Plus it has much less characters.
Puyo Puyo (series)
Rotate around these drops and create chains of four or more of the same color to make them disappear. Another timeless classic, with ports on too many platforms to list.
Puzzle Bobble (series)
Cool puzzle with the hero from Bubble Bobble, rotate your shooter and shoot the colored bubbles to line them with the ones descending to blow them up. Has a lot of shameless rip-offs on iOS and Android.
Risky Challenge / Gussun Oyoyo
Interesting spin on Tetris, you must rotate the blocks to create a way for the character to reach the door, as well as protecting him from harm.
Super Puzzle Fighter II Turbo
Cool puzzle with SD versions of Street Fighter and Darkstalkers characters, you must create colored gems by combining them. Create gems as big as possible, them blow them up with the bomb pieces to send lots of gems to your adversary.
No, there isn't a Super Puzzle Fighter 1, that was just Capcom indulging in some self-parody.
Tetris the Grand Master / Tetris the Absolute the Grand Master 2
1998 / 2000
Tetris on LSD! Trippy visuals and insane challenge, only for the hardcore ones!