I played 2048 a couple of years ago and I enjoyed it, although it seemed pretty basic and rather luck-based. At that time I'd read up on the game it was based on, called Threes. The two seemed pretty much the same in that the core gameplay is identical (pair up tiles to combine them and try to get the highest tile (and score) possible), so I didn't feel the need to rush and track down the original. But now having played both, it's clear that 2048 is an imitation of the real thing.
Threes is extremely polished and fun to play just on a visceral level. The presentation, sound effects, and background music are great, and the game shows you which tile is coming up next, which completely changes the way you approach it. I don't know how much the order of the tiles given to you is the same in both games, but the pacing of Threes seems way better. Basically tiles come in cycles of three main phases: 1 and 2 tiles (the lowest level), groups of 3 tiles, and every once in a while a higher tile that is selected from a set (e.g. 6 12 24) but is random. This pacing is clearly well tested and thought out and balanced, and the game has a really nice progression where in the first phase the board fills up quickly, but then they get cleared out in a satisfying way.
It's easy to waste hours playing Threes, and it's too bad that I recently posted my list of Favorite Puzzle Games of All Time, because somewhat to my surprise, Threes has earned a spot on my list. It's another super elegant, addicting, fun, and satisfying game, and it's currently free on Amazon's App Store, so there's no reason for puzzle fans to not pick it up and try it out.
Still-relevant links can be found on my post about 2048.