Drivers gearing up for trips this summer face escalating prices at the gasoline pump, an early sign that $70-a-barrel oil is starting to reach into consumers’ wallets.

Average U.S. retail gasoline prices are climbing toward $3 a gallon, the most expensive in more than three years. The national average was around $2.87 a gallon Monday. In states such as California and Washington, prices have already breached the $3 level after rising 24% and 17%, respectively, from a year ago.

Economic...