Catering is always the biggest chunk of any couples wedding budget. If you are on a budget it is always nice to find creative ways to cut costs without taking away from the quality of your wedding. While not asking for table cloths would save you a lot of money it would probably make things look a little ugly. But here is a better idea. Instead of having the caterers bring their own dish ware you can collect your own. Ask family and friends to use their china for your wedding. Gather mis-matched dinner wear and use it for your wedding! Mis-matching is totally "in" right now so you'll be a head of the game. ;) One of my brides did this recently and it was so lovely!
I think you could easily do this with silverware, cups and napkins. I am not a "stylist" but I'd say the key to mis-matching is them all having a few key elements in common. For example, if you are doing the plates make sure they are all round and are mostly white. Or for silverware make sure they are all silver and not gold or other colors.
Something you'll want to keep in mind is that sometimes things get broken, so if a family or friends lets you borrow these things make sure you let them know accidents happen. If they are someone's great-great-grandma's from the late 1800's I'd pass on borrowing them.
Another idea is to have a potluck. I'd only suggest this for weddings taking place outside in a rustic area. Have your guests sign up to bring a dish. Start by setting a theme to the meal. Italian, Mexican, American, etc. Make guest with last names A-C bring the main dish and so on with the rest of the alphabet. Have them sign up, so you know who is bringing what. Make sure to include how they will bringing their dish. Sometimes they may bring a crockpot that needs electricity Also, knowing this will help you know how much table space you'll need for all the dishes. Then have signs around the tables so guests know where to put the dishes they brought. The mismatched china may help your non-traditional catering really come together in this scenario.