I would say the two I use most often are Romano and Provolone, with Parmesan coming in at a close third. Cheddar would be fourth. We eat a lot of pasta dishes in our household, so I put Romano on just about everything, as well as soups and side dishes. Aside from that, Provolone is kind of my go to sandwich cheese, I put it on burgers, lunch meat sandwiches, etc... I also use it regularly in omelettes.
That's not to say that I don't like other cheeses as well, but their flavors kind of limit their uses. I wouldn't use Cheddar on a pizza for example, but I would use Provolone in place of Mozzarella. Also, most other cheeses tend to be too expensive to buy on a regular basis, such as goat cheese or blue cheese.