Depends on where you go in the US. Large chain theaters like your Regal and AMC will usually run trailers and maybe some partner company's ad but not much else.

However the local theaters will just have the equivalent of a slide show of ads until it's time to show the trailers and movie. Unlike the ad's that @gooddream was describing, these are only really just advertisements for local companies and sponsors. They're usually unobtrusive and i personally like seeing local businesses run as i prefer them whenever possible to large corporations.

Edit: for clarification, The local ads at the local theaters would run before the films start time, at the start time we'd see just trailers.