For instance, in Farmville you can't buy certain seeds, etc. until you 'level up' (move up to the next level in the game); and part of the criteria for leveling up is to have a lot of neighbors. Same thing in Farm Town. In YoVille (where you bake sweets for money) you earn more money for your bakes according to the number of neighbors you have. There are lots of other things you can do according to the number of neighbors you have.
The problem I have with the games is that I can't tell who's who because some players use different names in the games. The only way I can tell who they are is by their profile pictures. So here's some screenshots of how I'm trying to keep up with it:
It's a lot easier for me to tell what's what - because the games only allow so many actions, such as inviting friends and gift giving, per day. I don't want to waste gifts sending them to people who aren't active players. Inactive players are important as neighbors, but I like to send gifts to people who send them to me, etc.
It's something to do besides worry about home improvements....
