A thread on the White Wolf forums (here) concerns three Vampire players whose characters don't mesh. I've been there. When running Vampire at college, there was rarely a reason for the PCs to be in the same room, and as such rarely a reason for the players to either. Especially when the PCs' reasons sometimes clashed, so the players wanted to advance those in secret.
Some is fine - some is great, in fact. I was always happier with character-centric plots than mission-based games. I'd love to play a game as character-heavy as that at times. But there are limits. About a quarter of an average session, say. More than that and you should look at Skype.
(Happy 20th birthday, World Wide Web!)