Carry snacks. Having some snacks like granola bars, trail mix or even fresh fruit along can help save a lot over buying them from street vendors and convenience stores.
If you're traveling by car, stock up on bottled water and other drinks at the supermarket or discount store. A six-pack here will often cost the equivalent or even less than the price of a single bottle from a convenience store or street vendor.
Drink water with meals. Even without alcohol, soft drinks, coffees and teas can add a substantial amount to your check (especially in countries like Japan). Drink free water with the meal (as long as you're in a country that it's safe to do so). Buy soft drinks at markets instead.
Carrying along an immersion heater is great for making coffee, tea or instant hot chocolate in your hotel room. It can also heat instant soup or boil water for other purposes. This inexpensive travel accessory is sold at anywhere travel good are sold.
Have picnics! You can save a bundle by having impromptu picnics. Whether they be a late night snack in your hotel room or a full romantic meal against a spectacular backdrop like the Grand Canyon or the Eiffel Tower, picnics are a boon to the budget conscious traveler.