A cheese tray is a nice thing to have with many types of food. It's easy, it's nearly self serving and a few grapes, figs, and apple slices make a complete garnish!
Do you want hot things for appetizers, or do you want cold/room temp things?
There is a wonderful cheesy onion "dip" that is served hot. Crackers (a sturdy stone ground wheat) or bread (again a sturdy, hearty type) make good vehicles for getting the dip from the casserole dish to the mouth.
Grilled (you can broil them, or roast them in the oven) asparagus makes a nice appetizer. You can serve it plain, or wrap each spear in a small bit of prosciutto, or serrano ham.
If you like Pillsbury prepackaged products you can take the crescent roll tubes, press the dough into squares and cut it. Wrap it around asparagus spear pieces, or steamed (not overcooked) broccoli or cauliflower, a bit of cheese (Swiss is nice) with a dollop of mustard (wrap the whole thing in a square of dough) and bake until golden. I personally don't care for them, but I've seen folks rave about them at parties.
Mini calzones are nice. They take a bit of work (in that you spend some time making bite size ones) but usually are quite a hit.
Shrimp (or rock shrimp which we prefer) cooked in a well seasoned water, drained and served cold are nice. It's a bit different than the usual shrimp cocktail.
Oysters Rockefeller make an outstanding appetizer, but you need to serve them piping hot so it's not really convenient.
Little tiny potato pancakes, or little tiny crabcakes are usually a really popular finger food.
Don't underestimate the power of an excellent (albeit traditional) cheese fondue!

Uses up a ton of bread, and fills folks up nicely.
Lettuce wraps are quite popular. The trick is getting a lettuce that is easy to work with. Romaine can work, and so can some butter lettuces. Iceberg isn't so great.
Spicy garlic shrimp are wonderful, but can be messy (oily).
An assortment of olives is usually quite popular.
Strong dried meat like sopressatta, salami, pepperoni along with cheese (muenster, swiss, cheddar...) olives, lemon wedges, satsuma (or clementines, or tangerines) make a nice "plate." If you think your guests would like them, anchovies mix nicely with this combination. Have a good bread alongside.