Yep, the Bear & I eloped in December 2006. We hadn't been together very long (6-7 months), so no-one was really expecting it. We told absolutely no-one. We were going on a round the world trip anyway, and our first stop was San Francisco. We took a side trip to Vegas and got married in a brand new bright red Ford Mustang convertible which we hired for the few days we were there (the Bear wanted to bring the car home!). Everyone was great about it after the fact (what choice do they really have anyway?) my mum was briefly disappointed but she has never been particularly involved in my life so she didn't harp on it much. My stepmum (who I'm very close to) was disappointed cause she would have loved to be involved in my wedding. My dad was completely ecstatic because as far as he was concerned it saved him shelling out $50K for a wedding (which I would never have asked him to do BTW). My brother was the most shocked, we had seen him in Australia at Christmas, met him a week later in Spain and had got married in the meantime. The Bear had been married before so his family didn't make a fuss about it.
As to cost, apart from the flight (from memory around $2500 ish which was pretty standard then for a RTW ticket I think) and the car hire the costs were:
Licence USD$55
Wedding chapel USD $45
Tip for minister USD $60 (discretionary)
Cheapest wedding in history! Because we spent so little on the wedding itself, we could afford to stay in nice places in the States, Spain, Switzerland, England and Thailand over the course of the trip. We arrived in Vegas at 5 in the afternoon on the day we got married and didn't start 'organising' the wedding until we got to the hotel room, we were married by 7.30pm.
For us it was great - it was completely intimate, there was no big hoopla, no sense of pressure, no one else's expectations to manage. We were parked outside the Wedding License Bureau and we looked at each other and said "are we going to do this?". We could have just driven away and laughed about it, no one would have known anything about it, so there was absolutely no sense of pressure. We both agreed we would go ahead and do it, and we have never regretted it for a second!
I have a few friends who have eloped in Australia and have found that to be great too.
Good luck with whatever you decide!