http://www.imdb.com/title/tt0058815/
http://www.imcdb.org/movie.php?id=58815
A few surprises: yes, Tony Nelson (Larry Hagman) drove a GTO but other cars seemed to be supplied by Ford, and just about every truck in sight is an IH. No car supplier is listed in the credits.
These images come from the 1966-67 and 1967-68 television seasons if that helps with dating some of the vehicles.
ep. 2.3
1966 International Harvester B Series, two stars
2.5
1966 Pontiac GTO, three stars (Tony Nelson's car)
...and an alternate shot from ep. 2.6:
2.19
1966 Pontiac Bonneville, three stars (This is Dr. Bellows' car, he drives it in more than one episode)
Mercury Comet, one star
1967 Ford Custom, two stars
Ford Thunderbird, one star
2.23
1962 Buick (Electra?) convertible, one star
(in case anyone's interested, the car in the shadows appears to be a '64 Pontiac GTO)
2.27
Cadillac ambulance, two stars
2.31
1967 Pontiac GTO, four stars
Here's an alternate shot from ep. 2.19...It's supposed to be the same car but notice it has dog dish hubcaps instead of mag wheels. The car switches between these during the run of the show. Note Jeannie is driving it this time, we very rarely see her driving a car.
ep. 3.1
1967-8? Ford Mustang convertible, two stars
3.3
1967? Jeepster, one star
Rolls Royce, three stars
3.5
Dodge Power Wagon (M 37?), one star
Jeep, three stars
...and an alternate shot from ep. 3.20, note it has different wheels.
3.6
1962? Cadillac, one star
Volkswagen, one star
1962 Ford Falcon wagon, one star
3.8
1967? Cadillac ambulance, one star
International Harvester B-series?, one star
1967? Jeepster, three stars
3.9
1966-7? Chevy II? one star
1967 Ford Galaxie 500, one star
1964? Ford Falcon sedan delivery, one star
3.11
1960 Ford Sunliner, one star
unknown (moped or motorcycle?), two stars
3.12
1967? Buick Riviera, one star
1966 Dodge Coronet, one star
1966? Ambassador, two stars
3.15
International Harvester (Loadstar?), two stars
3.16
unknown forklift, two stars
1968 International Harvester C Series, one star
3.17
unknown vehicle, one star
1967 Ford Custom, one star
1956 Buick Century, two stars
unknown forklift (same as 3.16?), two stars
3.18
International Harvester Loadstar, one star
3.26
1968 Pontiac Bonneville, one star
1967 Ford Custom, two stars