There are shows with planes flying in formation (the Blue Angels); there are shows with motorcycles driving in formation (the Philly PD, among others); there are shows with clown cars driving in formation (the Shriners) – are there shows with regular-sized cars driving in formation?
Nascar?
ISTR that OJ Simpson made a pilot for a show like that. IIRC, no network picked up on it.
Joie Chitwood Auto Thrill Show may do what you’re talking about.
The correct term is a Shriner ‘Motorized Patrol.’ It was either that or join the band.
Automobile commercials.
Seriously? You should start an "Ask the … " thread in MPSIMS.
I’ve seen a clip of a Volvo (IIRC) team doing this. It was from a TV commercial, but I understand they put on displays as well.
You can see this show on I95 or the Schuylkill every weekday, morning and afternoon. Lots and lots of cars and trucks driving in slow formation. 
As mentioned, car commercials do this every so often. Here is a promo for the Saab 9000 that you can see online: http://video.google.com/videoplay?docid=8521999166042642874&q=saab
Since the question has been at least partly answered, I feel less guilty posting an only-tangentially-relevant link to The Red Barrows (A close-formation wheelbarrow display team).
There was no particular agenda behind the question, so I found the wheelbarrows delightfully relevant. Or irrelevant. Or whatever. After I wrote the OP I remembered a riding-lawnmower drill team.
There’s this “sport” called drifting, which came here from Japan, where cars compete in driving around a course sideways, turning right while steering left, tires smoking. Within this, there are team exhibitions. Just driving in close formation isn’t really challenging enough.
A vintage films program run here recently showed a 20 minute film taken in the mid-60s of the Chitwood show. It was fairly well underwhelming except for the close formation driving (and even that wasn’t really “thrilling.”)
I think they’re called “Toro, Toro, Toro.”
You absolutely have to see this video.
It’s quite good and very entertaining, but I just plain don’t believe there isn’t some mechanical and possibly cinematographic trickery going on there; the two cars skidding around on a wet surface while staying apparently locked together is probably the best example - there’s just no way they would both handle in such a way as to make that possible in those conditions; one of them would lose traction before the other, if only because the surface they’re driving on is not uniform.
For the life of me, I can’t figure out why there’s a google ad for a movie debating wether Jesus really existed or not at the bottom of this page.
Drifting…OJ Simpson…Wheelbarrows…Jesus. Oh, yeah, sure. I can see how that all fits.
It’s probably related to the ubiquity of the “learn humor writing from the pros” ad. Alas, I haven’t clicked on the latter yet, so I don’t have a joke at the ready here.
Excuse me Dances, but you are not by any chance in Little Chosy are you?