On that evidence, I wouldn't say aliens existed.
However I believe that life must exist on another planet. Be it a fully sapient species or a mere microbe, I cannot accept that in a galaxy - a universe! - as big as ours, ours is the only planet with life on it.
I find it incredibly arrogant to even suggest that we inhabit the ONLY planet with life. Granted, the conditions have to pretty damn specific and thus likely to be uncommon but out there, somewhere, there HAS to be life.
Do I believe that extra-terrestrial life has visited our planet before? Tricky one, that...
While I'm quite happy to chalk down every redneck's "experience" as a result of foetal-alcohol syndrome, if another sentient species were aware of us, they're in no hurry to show it. It could be that they saw our planet and went: "Oo! That looks nice...oh, bugger! It's taken!" and moved on. It's also equally possible they took one look at us, as a species, and thought: "Fuck me, what a bunch of c*nts!"
Short version: I believe but I also think they're nothing like what we expect them to be.
Wardy
PS - If, by some squillion-to-one chance the Asari really do exist, I would like to apply for the post of official Asari-Human liason officer right away!