When making your travel budget, don’t assume that lodging and airfare will be your biggest expense. Now, more than ever, rental cars are shaping up to be one of the biggest — and stubbornly high — aspects of people’s vacation budgets.

A summer road trip used to be a cost-effective, easy getaway. This year, soaring gas prices and expensive rental cars might make you think twice about hitting the road. According to the Amer...