The collection aspect in Pokemon is what really sets it apart (or at least it did before numerous clones appeared). Every single enemy you fight you can add to your "party". The whole concept goes beyond the usual "level up real high and save the world". The game plays in a much less linear fashion, focuses more on exploration than other RPGs, and best of all it isn't just about telling a story. The real goal in Pokemon is to "catch 'em all" not "find out what happens in the story".
With most RPGs when fans talk about it's "hey what did you think of the part where the hero's girlfriend gets killed?"
With Pokemon it's "hey have you caught one of these yet?"