Deviled eggs! You can't get much cheaper than eggs, mayo, and mustard. I've found it's one of those things that people don't want to admit liking, but they ALWAYS get gobbled up!

Other cheap ideas:
Olives--if you have a grocery store with an "olive bar," you can pick up an assortment fairly cheaply.
Frico (fried parmesan crisps)
Bruschetta (easily made by toasting bread in oven) with a marinara sauce or a bean-based dip
Pita with hummus or spinach dip
Quesadillas--you can make 'em fancier with whatever fillings you can afford
Finger sandwiches--crustless bread triangles with cream cheese or butter mixed with herbs, cucumber, watercress or nuts.
Bacon-wrapped water chestnuts

Wow, you guys! What great responses! Thanks! I have a few I can add:

roll-ups--take a whole wheat (doesn't have to be) tortilla, smear with cream cheese and pesto, or guacamole and shredded cheese, or anything else you think of. Roll the tortilla tightly, then cut into one inch slices.

Cheap nuts from Trader Joes. They have good-sized bags of honey roasted peanuts pretty cheaply. They also have other great sugared nuts, including some cinnamon almonds which are delish, but not so cheap if trying to feed lots of Holiday mouths.

My mother likes to unwrap and slightly warm a package of cream cheese. Then she puts it in a bowl, pours over it one can of black beans, one can of corn, (both drained, of course) and a jar of salsa. She puts the bowl in the middle of a large platter and surrounds it with corn chips.