Do I need commas in this sentence:
"The car which was a rare sports coupe was built in 1966."
There are two kinds of relative clauses; defining and non-defining (they may have different names elswhere).
Defining clauses give meaning essential to the meaning of the sentence, non-defiining clauses give extra, additional information which is no essential to the meaning of the sentence. So for your sentence here, you really need context to decide.
If there were other cars, for example, and the fact that this car was a rare sports coupe, you would not use commas. if it's just extra information about the car and it's not relevant to the fact that it was built in 1966, use commas.
There were 3 cars. The car which was a rare sports coupe was built in 1966, the car which was an old family car was built in 1967, and the car which was an old shit box was built in 1968.
The relative clauses here are essential to the meanings of the sentences as they help us define each car exactly.
Whereas if you say his car, which was a rare sports coupe, was built in 1966
, the extra information is not essential to the meaning of the sentence (you're really just expressing when the car was built; your meaning will work without the information that it was a rare sports coupe).
Another example from oh mighty Mr Callan:
I have two uncles who are very old.
This sentence means I have other uncles (I have two uncles who are very old, and two who are very young).
I have two uncles, who are very old.
This means I have only two uncles. The fact that they are old is just extra information here. The important information is that I have two uncles.
I hope this helps.