I like collecting things, and since Pokemon has so many Pokemon to collect (shiny, legendary, events, etc.) it keeps me interested. Plus I can bring my DS to university and play it between classes (can't say that for a Wii). The games also have a lot of possible things to do in them (collecting Pokemon for the Pokedex, chaining, RNGing, etc.).
I also like the global connectivity of the fourth and fifth generation games. You can trade with people all the way around the world, and not too many other games allow for that level of global interaction.
And they always come out with new stuff for me to waste my money on (that's probably not a good thing...).