Besides using up precious gas, a trip to the dump is never a pleasant experience. After your garage sale is over, however, unless you were lucky and managed to sell everything, you're going to have to get rid of your leftover things somehow. It may be that you have an excited relative who wants everything you own -- but it's unlikely. To avoid going to the dump, try one of these ideas to be rid of those last few bothersome things you simply couldn't sell.
Advertise your items as free on craigslist. The nice thing about this option is that you can tell people interested in your items that they have to come pick them up, and then you don't have to drive anywhere at all! Optionally, you can say that if someone wants your stuff, they have to take it all, leaving them with the responsibility of throwing out whatever they don't want from your pile of free things.
Find someone who wants the items as donations and will pick them up. Local organizations are often looking for donations for sales or their company's maintenance or what have you, and they're often more than happy to do the transportation so long as they don't have to pay for the items! Advertise on craigslist or seek out community service organizations in your area to see if they are in need of any sort of donated materials. Just don't give them any trash -- make sure the items you're donating are worthwhile.
Drop the items off at a Goodwill or Salvation Army truck. Both of the aforementioned organizations will often park big trucks at various non-store stations so that people can just drop by their things. These trucks are usually found in locations where you would be anyway -- Park & Ride spots, mall plazas, and outside of libraries are common places for them to park. You can wait to drop everything off until you're headed that way anyway, so it won't be an extra trip.
Work out a deal with a neighbor or friend. Offer to pay the dump fee, for example, in exchange for them making the actual (smelly!) trip, or exchange trips -- they go this time, you go next time. If it's someone you're familiar with, this might work out very nicely for both of you.
Hopefully, though, you don't have much left to work with when your garage sale is over! If you advertise on GarageSaleCow.com, you'll be putting your sale out there for other enthusiasts to see and visit!