So, Say you are in the Thieves Guild. Walking around town at night you see a shady character walk out of a house that you know isn't there house. Go talk to them, well look, it's a fellow thief. Better yet you sneak in that house to see them stealing. That would be amazing. In daggerfall I was attacked by the Thieves Guild while guarding a random item for 3 hours (game time).
The Fighter's Guild, to walk out in the wild to see a guild member fighting a bear or some bandits. Escorting merchants, wagons, etc.
A Mage's Guild member gathering outside, casting magic on things, interacting with their daily chores outside.
The Dark Brotherhood assassinating people (although this wouldn't be really easy to witness?)
Even though this may seem difficult, these guys don't even have to be important people. Hell, they can just be giving the generic name that they are a part of the X guild. In Oblivion it seems like a lot goes on inside of the housing for these guilds, but outside, not really. It would be nice to interact with your guild on the outside world and better yet maybe not even give them names. To know that the guild breathes on the outside would be refreshing. Not only that, for them to even help you out with something if you are in a tight spot, (like guards on monsters/bandits/bad people).