"Who cares, I have an infinite amount of money." — Bill Gates
Too bad, but that's not the case for my brother and me. Since we're both students, we had to make the trip as inexpensive (not cheap) as possible without missing the essentials. This means we didn't want to spend money on unnecessary things, and at the same time didn't want to save where it hurts.
This is a very subjective definition. For some people, sleeping in a tent in a national forest without the possibility of a shower every morning isn't worth the $30 savings compared to a cheap motel room — for us it was. On the other hand, we decided not to skip places like Disneyland "just" because the admission is $31 (+ $6 parking fee), which is horribly expensive but pretty normal for a whole-day adventure park in the US.
1995 prices All prices mentioned here are from 1995. Adjust for inflation accordingly — but the principles still hold.
The two major items on the budget are food and overnight expenses. If you can cut these down, you're very well off. We accomplished this by:
Buy at big supermarkets (philosophy: the bigger, the cheaper). Since we're not much of cooks, for dinner we mostly chose simple just-heat-and-eat spaghetti cans: ravioli, tortellini, spaghetti with meat sauce. When you get really advanced you can proceed to the Chinese 2-in-1 cans where you just add instant rice — tastes great!
At the end of our trip we got pretty tired of canned food and started eating at fast-food places. Taco Bell is our absolute favorite. Somehow it seems impossible to live in the US without getting kind of addicted to fast food. It's so convenient, cheap and — of course — fast. But not nearly as healthy as ravioli cans. ;-)
For in-between meals (we never really had a set lunch time, but ate when we were hungry) we often had sandwiches: Wonder Bread, lettuce & tomatoes, salami, cheese, Miracle Whip. For this purpose we had bought a cooling bag and a cooling element that was "recharged" whenever we came near a freezer. Apples, oranges, bananas and other fruits were also common in our diet.
Make friends through the internet.
This was our secret weapon. By posting on Usenet newsgroups before departure, we connected with dozens of Americans who offered us a place to stay. Not only did this save us enormous amounts of money, it also gave us the most authentic and memorable experiences of the trip. We stayed with college students in Atlanta, families in Virginia, fellow riders across the West. The hospitality was incredible.
Camp in national forests.
Camping in national forests is free (dispersed camping / boondocking). This is very different from national parks, where campgrounds typically cost $10–$20 per night. National forests have fewer amenities but you can't beat the price. We carried a tent, sleeping bags, and a small gas stove for exactly this purpose.