If it's a game or series I'm really into, I enjoy playing ports if I've already played one version of it over and over. Usually there's something exclusive to each version of a game, even if the overall game is almost exactly the same. It's those small, even minuscule differences that I enjoy coming across.
Here's just one example:
I own Tony Hawk's Pro Skater 3 for PS2, GameCube, Xbox, GBA, and N64. I had the PS2 version when it originally came out, I consider that one to be the definitive version of the game, but I've also played it to death and haven't revisited it on the PS2 in a very long time. So when I have the itch to play THPS3, I've gone after other ports just to get a different experience, even if that experience is only a slight hair different most of the time.
The Xbox version of the game does have a few noteworthy differences. The gameplay runs smoother overall and stays at 60 FPS better than other versions of the game, it has 5.1 Dolby Digital support, and best of all, an exclusive oil rig level not found in any other version of the game.
The N64 version, which is a port of the PS1 version which is pretty much a watered down version of the PS2 game, is different enough in many of the levels that I found it fun to see how the developers tried to scale the game down to be playable for the old systems. The N64 THPS3 is also historically significant as the final N64 game officially released in North America, yet another excuse to convince myself that I'm not a sucker for paying full price for the same game I already had on three other platforms.