I don't have any complete collections for one system and don't think I would ever want to. As others have already stated, there are a lot of crap games regardless of which system it is. I will pick up crap games, but only if they are dirt cheap or free. Hence why I got Kabuki Warriors for Xbox yesterday.
As for particular franchises, then
yes I do go for complete collections. Final Fantasy, Tekken, Soul Calibur, Ratchet & Clank....there are tons of great gaming series that I try to get every game for it regardless of the system it was released on.
I also collect games from certain developers. Naughty Dog is a good example. Just missing Way of the Warrior for 3DO by them.