During the course of "Cheers," how many vehicles (motor or otherwise) did Sam own? If you do the easy one, please try to specify model year and colour.

Corvette and the boat that sunk during his sail around the world....that's all I can think of.

And Sam's Corvette was a red 1966.

To help push this along, I can remember at least 5 vehicles. You have already named 2: a) the Flame Red Corvette; b) the boat he bought after selling the bar after season 5 to sail around the world, the boat that eventually sank.

That's 2 down and at least 3 to go.

Well I just remembered he drove a Volare. Possibly blue or something...

Correct, he drove a Volare in season 8, "The Two Faces of Norm," after selling the Corvette to Lilith.

3 down, at least 2 to go.

To help push this further along, another vehicle is alluded to in Season One's "Someone Single, Someone Blue."

To help push this still further along, the other 2 vehicles were not motor vehicles

I'm thinking of a Schwinn Bicycle.

Correct, as revealed in season 1's "Someone Single, Someone Blue."
1 more vehicle to go.

Considering how many times his penis has served as a rocket for women it counts as a vehicle in itself.
We've found em all! Samémon!

To help push this along one last time, I can tell you that the final vehicle was acquired from somebody else in the bar.

The final vehicle was another sailboat. Norm gave it to Sam in season 10's "Smotherly Love," to pay off part of his tab.