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.