I'm a Pokemon game fan, although not a traditional Pokemon fan (there's a slight difference). The things that draw me to the games are threefold (and yes, I own Pokemon yellow, blue, red, and green).
(1) There are few good turn-based RPGs that are handheld and the games fit the bill.
(2) The experience you have with the games are completely dependent upon your strategies with the Pokemon you collect. So, although the basic story and map are the same in each game, the strategies you use to go through them can differ greatly.
(3) The Pokemon I train and build up on my GameBoy can then be used for battle on my N64 as part of Pokemon Stadium. None of that "using the standard Pokemon" for me! It enhances the Stadium experience.
Now, I'm not discounting the incredible marketing ploy it was for Nintendo to make the Pokemon in each game differ, rather than putting all Pokemon in one game. All I am saying is that, for me, there was a reason to collect all the games as well as all the Pokemon.
I can't speak to MegaMan Battle Network, as I haven't played any MegaMan games later than NES.