I've never seen any story where Harry is raised by Slughorn, (not saying there isn't one somewhere) so...

The night that the Potter's were murdered, Lily Potter had invited Professor Slughorn over for some tea and to meet Harry for the first time. Instead of showing up on time, he got sidetracked (insert quirky sense of humor) and showed up moments after Voldemort's demise, holding a bottle of wine and a grin. Upon entering he finds the bloodied corpses of Lily and James and, being the genuine, caring person he is, decides to help Harry out of the goodness of his heart.

Taking him back home with him he plots to develop Harry into the perfect Slytherin: cunning, sneaky, scheming and most of all, concerned about his own profit.

Rules:

1. Humor.

2. Harry and Slughorn both are manipulative in the way that everyone knows they are doing it, but never realize it until after the fact, and still fall for it the next time. Harry is smooth and suave.

3. Harry, like Slughorn, cares more about his own gain than anything else. He'll want knowledge; he'll want power; he'll want respect; but most of all he wants a fat check.

4. He wants the best of everything, and though Slughorn doesn't spoil him (he'd rather have the spoils himself), he keeps him with better than average clothing, pocket money, before-Hogwarts-knowledge, etc.

Afterthought: Though this is not mandatory, I think the story would work best to skip around: miss pretty much his entire childhood, write the sorting and important events from the first few years, and then move in to more detail once Harry has reached the age of seventeen.

 

That doesn't sound much different from other Harry stories in which he is raised by a teacher and then goes on to acquire characteristics of the teacher's lifestyle. Examples that come to mind are Moody, Snape and Lockhart (actually I'm not sure I've seen a Harry raised by Lockhart yet - thank God).

The uplifting point here IMO would be Harry's obssession with a fat check. I haven't seen enough greedy!Harry around. Other than that, I like the idea of fastforwarding to Harry's late teen years. Although I wouldn't mind a chapter or two of the adventures of little greedy!Harry as he gets caught his hand in the jar.

 

Are you kidding? Lockhart!Harry would be fun! Consider the possibilities. Lockhart, instead of stealing other people's accomplishments, has Harry to beat down all the evil dark creatures. Both of them are fantastically vain, they compete for the "Most Charming Smile" award, and so on. I'd like to read that.