I think it's entirely possible that aliens visited Earth in the past. Some of the cave drawings depicting possible astronauts and ancient structures that they can't figure out how they were built make the show very interesting at times. However; there are some crazy theories that even a nutjob wouldn't believe.
I think we ought to expect that we are in one of the most simple universes that support sentience – should the universe be any more simple, it would have been pretty unlikely for sentient beings to appear, should the universe be any more complex, it itself becomes unlikely. If that's true, I'd expect that there's some difficulty still in sentient life forms appearing here, so they wouldn't be exactly all over the place.
In which case I'd expect no visits, possibly not even future contact – hey, if the closest aliens are in Andromeda, we've got one chance in a several billion years to meet them, and we are most certainly going to miss it. That totally sucks. Lately I kinda given up any hope for aliens.
Hopefully future studies on evolution and abiogenesis prove me wrong.