Thanks for the request, and hopefully I can convince you that we're not nutjobs at all (well, much) ;) Lots of proof and awesome links at the bottom...
So I am an astrobiologist, but because we haven't actually found any life in space yet, like most other astrobiologists I spend my time looking at the only examples of life we have: that stuff here on Earth. So my job title is actually 'palaeontologist and astrobiologist' - I look for and study the earliest fossils in Earth's most ancient rocks, and use them to understand better how and where we might find them in space. But astrobiology, or exobiology as it used to be called by NASA, has so many completely different branches, so there's no such thing as a typical alienhunter. You might have people who are investigating how much radiation a creature can take, or you might have people looking for inhabited planets around other stars. Myself, I look at how we can recognise the patterns and remains of microbial fossils, in the hope that we will be able to recognise them if they are there on Mars. I'm also about to start a project with NASA too that will use algae and bacteria to help make human inter-planetary travel a tiny bit more feasible. Ask me about this and I can give you the grisly details!
Will we find life? Well, as most scientists seem to think, and I'm not expert, space is pretty much infinite (at the very least, it's really really really big). And when you have infinity space and time, you have infinity possibilities, so it seems inevitable that there's life elsewhere out there, and because the universe is much older than our planet, it could well be as intelligent, if not more intelligent, than us. But because space is so incredibly big, our chances of being able to detect it are diminshingly small. Hawking's dangerous aliens might be out there, but unless they've found a way of breaking physics, they are millions of light years, and hundreds of millions of years of travel away from us. What we're more likely to find is microscopic, primitive life, on the planets and moons of our own solar system - because we can actually get there to study them!
NASA's mantra for looking for extra-terrestrial life is 'follow the water' - and in the solar system there's only a few places where water and other chemicals exist as liquids that life needs... In Jupiter's moons Europa and maybe Ganymede, there could be vast underwater oceans with life, and Saturn's moon Titan has lakes of methane that could be home to some weird methane-based microbial aliens. Mars is a target for looking for life, even though it doesn't have liquid water on the surface now, because it has clear evidence that there once was, and there may be interesting fossils on Mars like the ones on Earth. Also, it's close!
I became an astrobiologist because it is a subject that is super sexy! Everybody is curious about whether we are alone in the universe, and we all share a sci-fi dream of travelling the stars and investigating other life forms. My research started with the early fossils on Earth, but it seemed natural and incredibly exciting to apply my observations and experiments to potential fossils millions of miles away!
Here's my twitter where I do similar in 140 characters
I recently nearly won the UK-based I'm A Scientist competition in the Space Zone. You can read mine and others' answers to kids' questions about space.
And here's a paper I published on life on/in the moons of Saturn and Jupiter, in the fairly controversial (and hideous) online Journal of Cosmology.
EDIT Thank you all for the overwhelming response and for getting me onto the front page. I am a bit obsessive and I will be answering all your questions, so keep watching this space. For now though, I'm afraid this astrobiologist must sleep, but I'll be back on the case in the morning!
EDIT2 Still working my way through all your amazing Qs. Will take a while as I've got the lurgy and a couple of deadlines looming, but hang on in there and I'll get to you!