[Lucas89]

The way I think of it is this:

彼は図書館に行っている
He went to the library and is there now(or will be there maybe?)
so the action was completed and he is existing there now being the いる

彼は図書館に行った
He went to the library
Doesn't necessarily mean that he is there currently

Again this is just how I think of it so I could well be wrong since i haven't used it much before, but this is how I have thought of it for a long time now.