Many non-native speakers try to speak with an American accent by strongly pronouncing all the r’s. Experts refer to the typical American accent as a rothic accent, as compared to a non-rothic accent such as British English. A nice example is the word hard, which is pronounced as [hɑːd] in British English, but [hɑːrd] in American English, listen here.
Leaving aside personal preferences (I much prefer a non-rothic accent, it is so much easier on the ears), it is important to realize that you cannot just put an r into any word to make it sound American. A good example is the word idea. The British pronunciation is [aɪˈdɪə], whereas the American pronunciation is [aɪˈdiːə]. However, you can quite often hear people say [aɪˈdiːər],
which is generally wrong unless you happen to be on a pirate ship. If you are interested, I came across a very useful post on how to pronounce r the American way here. There is also a phenomenon called the intrusive r, referring to the insertion of r’s in order to avoid two consecutive vowels.