I've recently started playing "Threes" on my iPhone and iPad, and it's a fantastic puzzle game. Almost everything you do in the game is done via sliding gestures, so it's a beautiful, if minimal, interface. The game itself is a 4x4 grid, that starts out with only some occupied. You slide tiles either vertically or horizonally, which all tiles that aren't running into a wall moving in that direction. When one hits a wall, if two tiles can be combined (more later), they merge into one tile with a combination of the values of the two.
That's the whole game; it goes until the board fills, and there are no combinable tiles.
So it's very simple in concept, but the strategy is pretty complex. As far as how they combine: two can combine with one to make three. And any number can combine with an identical number to make double that number. So 3+3=6, 6+6=12, 12+12=24, etc.
Scoring is done on a log scale, adding 3 raised to the log3 of each tile (two and one both score one point) together. So a three tile scores three points, a six scores nine, a twelve scores 27, etc.
Like I said, simple. But very difficult.
Really, the only thing I can complain about with the game is how long the opening animation runs. If it was cut in half (and, it just now occurs to me, the age of my iPhone 4 and iPad 2 might factor into this), it'd be much better.
But it's easy to get past that. Very fun game, and I just love the interface.