If you define an "alien" as anything that, by our earthly definitions, is alive, then it stands to reason that they do in fact exist. However, the first definitive discovery of extraterrestrial life won't be anything that's like us; the first discoveries will be more on the order of bacteria or viruses. Already around the moons of Jupiter there's evidence that liquid water exists -- and that is the first and critical determining factor to finding anything that has life processes like our own. Mars may also have water in liquid state under its surface; for that matter, also the Moon has had ice discovered in deep crevices, and maybe there's water further down.
As far as the Vulcans or Little Green Men showing up on terra firma, that's not likely to happen anytime soon, if ever, with our current understanding of science and physics. If, in fact, (and not science fiction) we're able to leave the Solar System easily, and visit other Earth-like planets, then there's a good chance we may even find life developed on par or above humanity. See links for the Drake Equation -
Statistically, it makes sense that there should be other forms of life in the Universe. Just take a look at the Drake equation. it sets up parameters for narrowing down hospitable planets and calculates a theoretical number of planets that have life. Granted, these life forms will probably be nothing like us. There is a good chance they are not carbon based and will not need the same things we need to live.
Yes I believe that aliens exist because in this vast universe only one habitable zone its not possible. Its not important that aleins can live only in oxygen I think some other organisms can breathe hydrogen or other gasses.
I believe that because God only has one son and he chose to send him to earth, we have been set apart from anything else that God created. I suppose it is possible that there is some sort of life on another planet but we can never be sure. All I'm sure of is there is nothing like us.