Courtesy of The Aviationist, here's a great video of a Lockheed U-2 spy plane (often referred to as the "Dragon Lady") landing at RAF Fairford in England a few days ago. It shows the chase car following the aircraft down the runway at about 140 mph, its driver talking to the pilot on radio to tell him how far off the ground the plane's wheels are (he can't tell from the cockpit due to poor visibility). Unusually, in this video there's a truck following the car - something I haven't seen before. (The car driver, or in this case perhaps the truck crew too, attach light, flimsy wheels to the outer wings before the plane taxies back to its hangar.)
Apparently the chase car drivers (and presumably the chase pickup drivers too) have to undergo special training to handle their vehicles at very high speeds, while coping with the jet blast from the aircraft immediately ahead of them. It must be one of the more enjoyable jobs in the Air Force, if you ask me - getting paid to drive a sports car at high speed. You'll find more details here (including videos) of the U-2 landing, and the chase cars in action.