Romney wins the popular vote, but loses the electoral college
Neither candidate gets the 270 electoral votes necessary to win; House determines the President
Neither is particularly likely, but obviously the first one is the more likely scenario of the two you've listed. The first one is at least plausible; the second is extremely unlikely. In fact, if the election were held today and the states all broke exactly the way that they're currently polling, your first situation would actually happen. I doubt that it'll actually happen on Election Day, but it's not out of the realm of possibility.

There is only one plausible configuration of states that would result in an exact 269-269 split: Obama wins all the blue states (I'm counting Wisconsin as a blue state) as well as New Hampshire and Ohio. Romney wins all the red states and all the other swing states. I think it's EXTREMELY unlikely that that exact electoral configuration would come to pass.