Panic Bomber World (SNES)

Panic Bomber World is a puzzle game starring Bomberman. It's of the "falling stuff" and "versus" sub-genres. It's pretty good.
It's more complex than most games of this type. You do mainly play by matching up coloured Bomberman heads in rows of three, but that's where the genericity ends. When you match up rows of same-coloured heads, bombs spring up from the bottom of your pit. Every now and then, a lit bomb will fall down into your pit. When the lit bomb lands, it explodes with a traditional Bomberman plus-shaped explosion, and also like in bomberman, any other bombs caught in the explosion also explode like this. Any Bomberman heads caught in the blast don't disappear like you'd expect them to, though. What happens is that the traditional versus puzzle game junk blocks start appearing from the bottom of your opponen't's pit, and the more heads caught in the blast, and the more bombs that go off, the more junk blocks appear. The junk blocks can only be erased by blowing them up with bombs. There's also a red bar next to each player's pit, and when this fills up, a huge bombs falls into their pit and completely erase the top few rows of stuff.
In single player mode, you go to various countries around the world, fight two enemies, then a boss. I don't know how many stages there are, as i've only made it to the third boss so far.
Like I said at the start, this game is pretty good. It's not as good as Super Puzzle Fighter or Magical Drop, but it's still worth playing. If you're a big Bomberman fan (Bomberfan?), even more so, as this game contains tons of cool little variant Bombermen. Although the two "regular" enemies on each stage are just strange blobby things, each stages's boss is a Bomberman themed to whatever country that stage is set in. Jamaica has a laid back rasta Bomberman, America has a cowboy Bomberman, and england has... some kind of awesome badass Bomberman whose battle theme is some cool 16-bit power metal! As well as the bosses, the pit backgrounds also show Bomberman getting up to nationally-themed activities, like lying on the beach or going snorkelling in Jamaica, and having afternoon tea or looking for the loch ness monster in England!
Apparently, this game has also been ported to PSP and Wii.

Logic Pro (Arcade)

There are lots and lots and lots of picross/nonogram/oekaki logic games in the world, and this one is the best of them. The reason for this bold claim? Because this is the only one to actually make a game using the puzzles. This was the first game of this type I ever played, which was a bad move, because every other one has seemed poorly thought out in comparision. The reason being that every other picross game I've played has just been a collection of puzzles on a disc/cartridge. At most, they might save your best times so you can go back and beat them. Of particular note is the GaoGaiGar Oekaki Logic game on DS, which doesn't even do that, and lacks the ability to cross off squares on the grid which you know to be clear. There are two main commands you need in a game of this type, and it forgets one of them. Not to mention the fact that the puzzles never actually get harder. You do get 20x20, 30x30 and 40x40 puzzles in that game, but you only ever tackle them as huge sets of multiple, very easy 10x10 puzzles, and the whole thing becomes a test of your patience.
But anyway, back to Logic Pro. Look at the screenshots. You can clearly see two things that are very important to this game's appeal: the score and the timer. I said earlier that most games of this type have a timer. The difference here is that the timer in logic pro goes down, not up, and if it runs out, it's game over. If you make a mistake, you lose a big chunk of time, and conversely, for every correct mark, you regain a small amount of time. You also get a small amount of points for each correct mark, and a bonus for clearing a stage without any errors. The simple addition of a score and a time limit are what turn a picross game from a laborious slog into a tense speed puzzle, and it works.
You might have noticed the little caveboy in all the screenshots. He isn't just there for decoration, this game has a plot! In a harrowing and emotional attract sequence, we see a large pink ape crying to our caveboy hero and his red-haired female friend (player 2's character in the completely pointless co-op mode), loudly stating "I WANT TO BE A BEAUTIFUL WOMAN!", to which the brave kid yells "I CAN HELP YOU", and then goes off to solve puzzles, I guess. He mostly just stands there at the side of the screen, occaisionally jogging on the spot or shouting "GREEN LETTUCE" for no obvious reason. One last thing worth mentioning about this game, if you look below, you'll see that one of the later puzzles bear an eerie resemblance to famous child-killer Myra Hindley. I can't say whether or not this was intentional, though.