Alright I can't speak for people living in souther states (below North Carolina) where the red imported fire ant can be found or out west where it's found along side with the Argentine ant.
Up north where we are though I don't think there are any ants that could be considered a threat to the hive. Adult ants don't eat much, and can go a month or two without food. The hunger of the colony is driven by the larva which eat protein rich food, insects. Outside the hive you'll see them picking off the bees who's wings have stopped working, usually in the spring after clean up when they toss out the dead.
ExampleThey're so devoted to the brood that they incubate them whenever they can. Usually this is under stones or logs outside. Some species are more nematic than others though and I can see them as being a real problem, but usually not enough to kill the hive.
Acrobat Ants,
http://img.photobucket.com/albums/v735/mrilovetheants/Ants 2010/CrematogasterAppleAphids.jpgCrematogasterNote the heart shaped abdomen that comes to a point, and how they can flex it up over their head like a scorpion. They nest in hallow wood cavities such as the attic to a beehive. And they form sub colonies with continuous foraging trails linking them great distances. I had a colony of these ants living in the attic to one of my hives, with the foraging trail extending across the full length of our fence both ways and through several neighbor's yards, with sub colonies (pit stops) all along. I used shortening (the creamy white stuff) around the outside of the supports. As for the ants inside I just dumped them. Take the bee brush and scoop em out. These ants are bad because they eventually start digging into the wood they inhabit. The colony eventually moved on.
The Odorous House Ant, Tapinoma sessile
Tapinoma sessile scatteringNotice the bullet shaped abdomen. (And I could go on to say they lack spines, only have one waist segment instead of two, the eyes fall lower on the head but that's not that important.) To really clinch the ID, crush a few and they should smell like blue cheese or "rotting coconuts." The odor is only smelled after you've crushed a few.
These are another opportunistic nesting ant. Just like Acrobat Ants I've found these in the attic area of my hives nesting. They're easier to get rid of, just toss em and take your bee brush for the rest. The colony will move, even if they don't get the idea the first time. Usually they aren't a problem but an odd thing is happening. Colonies of this native ant normally have multiple queens (similar in size to the workers) but colonies get bigger as they occur in urban areas, while rural colonies remain divided and small. Really they're just an issue for city beekeepers and maybe suburban.
Those are the only two ants I really see as a problem to a beehive.