I think that the only real difference between вокруг and кругом is that the former can DIRECTLY specify a place around which the "circle" is. To clarify:

Вокруг дома никого не было. It's a very good sentence meaning that there was no one around the house.
Вокруг никого не было/Кругом никого не было - Also 2 good phrases meaning that there were no one around.
Кругом дома никого не было - No, this is bad. Кругом cannot be used to specify a location. I think it points at your location by default or at a location around which the action is being taken.

In other, more grammatical words - вокруг can be both a preposition and adverb, кругом is an adverb only, at least in its modern usage. As I also remember examples of its prepositinal usage in "old" texts, as @Alex80 noted above. However, I think this is either regional or "folk talk".

Quote Originally Posted by Alex80
Anyway it sounds strange for me 'обошёл кругом домика'.
That's because it's a badly composed sentence. "обошёл кругом домик" would sound a whole lot better, don't you think? Note: that кругом would relate to the verb in that case and not to домик, adverbial relation.

Now that I think of it, this preposition adverb thing opens up some room for creativity.

Они уселись кругом вокруг костра - this would totally make sense Although, no one would say it like this as кругом becomes absolutely redundant in that case. But that still makes total sense