Where I did undergrad, there were 2 options for honors -- Honors College or honors thesis. I didn't go the whole honors college route, but I did do an honors thesis. Basically, that's where you find a professor to work with and do an independent research project, usually in your last year at university. I obviously think that is a much more rewarding option, at least if you're interested in going for an advanced degree after getting your BA or BS degree.
My college doesn't have an honors program but instead has 5 year masters programs in several areas. I'm doing the 5 year masters in political science while getting an international relations degree at the same time. The reason there's no specific honors program is because the school sees the whole school as an honors program in a sense. Several other schools are similar. It really depends on where you go. You could go to a pretty average school but get an elite education from their honors program. For instance, UGA is a pretty decent school but not considered a "top school", but their honors program is on par with schools like Tufts. It also looks great on a resume depending on the career you plan to take or if you plan on going on to grad school. Really, it just depends on what you want to do. But as a perk, many schools offer better dorms, big scholarships, and more laundry machines in honors dorms than they do to other students.
