I think SJ's point is being missed. He's talking about getting the same game for two systems: the same game, not remakes.
It's not often that any games I get or want are ever released on multiple systems. I have few games like that, including Tetris Attack (SNES version) and The Legend of Zelda: Twilight Princess (Wii version). Those might actually be the only two, I'm not sure.
Remakes, yes, I love remakes. But the remake has to have something good about it that makes it worth buying, if I already own the game. Usually the reason is that the game is a portable version of an older game (Super Mario Advance series and Super Mario 64 DS), but I'd also get a game if it were remade with better control and or graphics (imagine an Ocarina of Time remake with Twilight Princess-quality graphics and improved TP-like control on the Wii). Since getting Super Mario Bros., I haven't gotten any games I already own.
And in the case of Pokémon, I used to always get both (sometimes all three) games in the generation. None of my friends were ever really into it except for the time when we went to an evil elementary school that didn't allow us to have Game Boys on campus, so I always have had to trade with myself. I'm sure if I went to them now and told them this they'd realize how many lives they've crushed... but now I only have Blue, Gold, and Ruby. This is really different from the case of Mario & Sonic, however...