Definitely book it before you go. I remember a story recently of someone who had a 50% discount voucher from one of the major car hire companies following a complaint the previous year. They took it to Vegas expecting to get a car at a hugely reduced rate, but actually because they just turned up on the day, they ended up paying MORE, even with the discount, than what they would have done if they had booked prior to travelling.
We used
http://www.dollar.co.uk for all our travelling during 7 weeks in the USA back in 2006 and pretty much all our travelling since then bar booking direct with
http://www.hertz.co.uk last year in New Mexico. Lots of people use the companies mentioned by Luci/Lesley, so I would shop around, but don't discount going direct.
I like the fact in Vegas you can pick up from your hotel and drop off at the airport, thus saving a taxi fare when you are due to fly out. That's why we always time our car hire for later in our stay in Vegas, not only for that, but also because we will have walked our feet to near death by that point.
Finally, also check Hotwire for car deals as well.