I do believe that aliens have visited our planet and have patrolled our skies, and I believe that they have been here for a quite a while. The reason I believe so is based purely on a scientifically-and-logically-driven train of thought-not a tinfoil hat conspiracy, either. I'm not here to tell you that there are aliens among us and that the all the world's governments are in cahoots to suppress the evidence of our extra-terrestrial watchers. I personally believe, at this point, it's logical to assume that they have visited us on numerous occasions. The physicists and astronomers have laid out numbers which support this idea, as well.
I am a philosophy and science student, and an atheist. This means I'm very skeptical. Being a skeptical logic-and-science-driven atheist, I am around many, many other skeptics who strongly believe aliens haven't visited us. The common arguments I hear against ET having been here, quite honestly, get under my skin. These arguments in opposition are always as follows: "The universe is too big for them to travel those vast distances" and "We're insignificant to them, why would they want to visit us?". I think this is a cop out. I think this is short-sighted and shot through with modern intellectual human logic. How dare we even try to apply this sort of logic to a civilization which could be thousands-to-millions of years ahead of us both socially and technologically?
Astronomers estimate that there are 200-400 billion stars in our Milky Way galaxy (http://www.universetoday.com/22380/how-many-stars-are-in-the-milky-way/). Each one of these stars houses a solar system with potential life-bearing planets. Thinking this through, without even doing any math, you have to believe that our galaxy is teaming with life, whether it be microbial or advanced. After critically and logically thinking it through, we can also apply a formula to it. Thankfully, a graduate student named Duncan Forgan of the Royal Observatory, Edinburgh, in Scotland developed such a formula. Here is a quote from the article which explains his findings:
"His model relies on current observational knowledge of stars and planetary systems, as well as some assumptions about the viability of life and its ability to evolve into an advanced, intelligent form. If life can only arise under a narrow set of initial conditions, Forgan estimates there should be 361 advanced, stable civilizations in the Milky Way. If life can spread from one planet to another through biological molecules embedded in asteroids, though, the number jumps to nearly 38,000." (http://www.scientificamerican.com/article.cfm?id=how-much-intelligent-alien-life).
Mathematically, anywhere from 361 to 38,000 advanced forms of life exist in the Milky Way. This means, that in our galaxy, there almost definitely exists a large number of advanced extraterrestrial civilizations with capabilities that some of earth's brightest physicists can't even comprehend. These aliens would have the technology to warp the fabric of space in order to travel through wormholes, teleportation, force fields and, perhaps, time travel (physics tell us that these are all possible). Beings this advanced would have no trouble traversing vast distances of space and charting the stars. Look at what our earth astronomers have accomplished studying the skies. Do you think a super-advanced alien civilization residing in the Milky Way wouldn't have the entire thing mapped and charted? Give me a break.
As you can see, they can theoretically make it here. Why would they want to travel to earth? Who knows, maybe it's morbid curiosity like a little kid watching ants carry bits of food into an ant hill. You think we're insignificant to them? Says who? We're a rapidly advancing species capable of amazing technological leaps, advanced weaponry, global communications, and space travel. And even if we were "insignificant" to them, might they possibly want to study us? We study bacteria, viruses, and parasites, do we not? Are these forms of life not vastly inferior to us? Or, possibly, them visiting us is just sight-seeing. Perhaps they find our earth pleasant to look at. Maybe for them, being sight-seeing mariners of the universe is as easy as a human putting on a pair of hiking boots and going for a scenic stroll.
I know the universe is vast and seemingly unfathomable, but it's almost certainly teeming with intelligent life. To say otherwise would be ridiculous. Look how far we've come in the last 100 years. Imagine how technologically advanced we'll be in 500 more years. Heck, imagine a civilization that has had thousands, hundreds of thousands, or maybe even millions of years to evolve. They would literally be god-like to us. A civilization of magic.