I'd say Shane pretty much hit the nail on the head with his answer. For most verbs, it is completely necessary to pronounce the "r" in order to avoid confusion with the infinitive or imperative. Take the verb "går" ("to go") in the following three examples:
Jag går. (I go/am going.)
Jag kommer att gå. (I will go.)
Gå! (Go!)
In the first example, you cannot drop the "r", as it would sound grammatically incorrect, as if you forgot to conjugate the verb. There is, however, one example that comes to mind where the terminal "r" seemingly disappears in everyday speech, and that is in VSO constructions (such as with questions or conditional clauses) where the verb is followed by the pronoun "du". Compare the follow:
Går du? (Are you going?)
Gå du! (Go, you!)
In the first example, I would say something similar to "gå'ru?", were the "r" and "d" merge to something similar to an alveolar flap (similar to the sound "tt" makes in the American pronunciation of "better"). This makes it slightly difficult to hear the difference between the two, though there definitely is one.
That being said, there is one verb that comes to mind that pretty much always loses its "r", and that is "är". As the infinitive form is "vara" and the imperative is "var", there is no risk of confusion. Depending on the dialect, it can be realized as either /eː/ or /ɛː/ in everyday speech. Nobody will misunderstand you if you pronounce the "r", but natives rarely do, unless they are speaking very carefully.
Hope that helps. :)