How do you respond to questions like "Have you ever observed a UFO?" This is a question that astronomers get asked by the public regularly, and I'm curious to see how others respond.
 A: When I get this question, I usually respond with:  "Sure, all the time."  And then I point out the nearest plane, satellite or other bright object moving across the sky at the time (there always seems to be one) and say "See there's one right there, I have no idea what it is exactly so it is unidentified, flying and some sort of object.  A UFO by definition." I then go on to point out as Geoff mentioned that UFO does not mean aliens.
A: "Yes, I have! I was at a public outreach event on a gorgeous clear night and everyone was pointing out the usual suspects to the public when I noticed a light flashing every ten seconds or so. I looked at it long enough to confirm and then said 'What's that flashing light?' And someone instantly said "It's a plane." And I said, "But it's not moving. I've been watching it for a minute." And I pointed it out with my laser and more and more people started seeing it. And it was so slow moving that I actually got it into my refractor's FOV and could determine that it was bright-flash, slow-flash... And no one could figure it out. And then it went away. And a few minutes later someone snapped their fingers and said, 'It was a booster rocket tumbling back from orbit! It was still in the sunlight until just now...' " 
I like to tell that story because it ends with a 'mundane' explanation that was still pretty darn cool! 
A: I have observed the sky for over 50 years and, yes, I've seen one object which was a UFO at the time. I was helping conduct a public showing with the observatory at the University of Maryland, College Park, in the early 1970s. I was outside the building identifying stars for people when I noticed a first magnitude star that wasn't supposed to be there. Of course, you think it might be a bright nova, but after a few minutes it started looking a bit extended, like a planet through a telescope. A few minutes more, and it became clearly fuzzy and, as it continued to expand,it gradually became weaker. Eventually it became larger than the Moon but fainter and fainter until it could be seen no more. Well, I was stumped.
But a couple of months later, I was reading Sky and Telescope magazine describing one of the Apollo Moon missions and how it had vented it's no longer needed propellants about half-way to the Moon, just at the time we had been observing!
So, 1) Yes, I saw a UFO! And, 2) it was a travelling spacecraft!
But, it they were not from another planet but were American astronauts.  
A: Typically, the questions I get are people who insist that they've found a UFO in some of the images that my work distributes, but that we're covering up because we removed the image and replaced it with one 'without the UFO' ... although, they rarely mention it directly, they just want to know why the image has been replaced.
I first explain to them that we remove the reduced and compressed 'space weather' images as soon as we receive the less compressed images from the main downlink, and reference the pages:


*

*http://stereo.gsfc.nasa.gov/artifacts/artifacts.shtml

*http://stereo.gsfc.nasa.gov/artifacts/artifacts_beacon.shtml
Most people are satisfied at that.  I've had a few where I've had to point them to the original FITS files, and point out that the ones corresponding to the JPEGs they were looking at were 512x512, while the replacements were 2048x2048... and tell them where to download DS9 so they can view the raw images themselves (and tell them to use log scaling).
My boss seems to get the more interesting feedback from people who are less easily convinced. (I only get them because I'm one of the people who get the mail from the address that used to be on our 404 pages.)
A: In 54 years of observing the night sky, with 1466 logged observing sessions and thousands more unlogged ones, I have seen a total of 0 (zero) Unidentified Flying Objects. I have logged the Sun, the Moon, 2 total solar eclipses, 1 annular solar eclipse, several partial solar eclipses, many lunar eclipses, 1 transit of Venus, 3 transits of Mercury, dozens of artificial satellites, all 8 planets, 2 dwarf planets, more than a dozen asteroids, many comets, many aurorae, hundreds of meteors, over 100 double and multiple stars, 238 variable stars, and 659 deep sky objects. In all that time I have not seen a single object in the sky which I could not identify.
Of course UFOs exist. People are forever seeing things in the sky which they can't identify: Venus, Jupiter, airplanes, satellites, meteors, mirages, Chinese lanterns, etc.
Many people confuse UFOs (things seen in the sky) with aliens (living creatures from another world). Not the same thing at all!
UFOs are usually unidentified because the observer lacks the astronomical or meteorological knowledge to identify them. That's why you never hear about UFOs observed by astronomers or meteorologists; they're only reported by people who are unfamiliar with what can be seen in the sky. The job of the astronomer is to help the observer identify what they have seen.
Although life almost certainly exists elsewhere in the universe, the immense distances between stars makes interstellar travel a practical impossibility. No scientist has ever been able to examine a real alien, so all descriptions are nothing but fantasy.
Ian Ridpath provides excellent clues to identifying UFOs:
http://www.ianridpath.com/ufo/ufoindex.htm
These links are interviews with eminent astronomers of two different generations on the subject:
http://media.abovetopsecret.com/media/3850/1966_interview_with_Carl_Sagan_about_UFOs/
http://www.wimp.com/believeufos/
