For starters, if you talk to Ysolda in Whiterun, she tells you she needs help getting her business started. You do her little quest, and help her get on her feet. She tells you she wants to buy the Bannered Mare. If you go into the Bannered Mare, the innkeeper tells you she's been thinking of selling to Ysolda. But... that's it. That's the end of that topic, and nothing ever happens. I would love to see a quest you could do, maybe a followup for Ysolda, or a new one for the innkeeper, that allows the inn to change hands.
And how about those guards? They want you to enchant their swords all the time, but you never get the chance to say "yes." Why not? How about I give him a quest, bring me 2 filled soul gems and I'll enchant your sword.
Those are just the two silly examples that came to mind after I created a new character last night. Can anyone think of a few more? There are tons and tons and tons of little events like this that could be built up into their own quests, so much that I'd happily pay for an entire DLC pack for it.
...Sigh.