I'd really like some other heroes in Skyrim, especially some of my own "minor" characters. There is a mod for PC gamers on the Nexus which adds different heroes with their own adventurer life btw.
I'd like to see this implemented. You see the occasional mercenary, farmer or pilgrim wandering around and it gives you the sense that things other than your goal are going on, but it's not really enough I don't think.
I want to see a group of scavengers wandering around with their most recent score of gold, a caravan rolling by with passengers aboard (which I could call to stop if need be) and that NPC I saw in the tavern in Whiterun heading back home after a drink. Not to mention, as has been said, various heroes heading forward on a miraculous quest to earn honor and glory.
The idea of having interconnected saves might be a bit complicated, and what would happen if your character was attacked by a bear and killed? O.o