You can wash it of course...there may be some precautions with automatic car washes...I always do it myself at home or in one of those insert-your-quarter places.
Surely washing the car is a job for your valet - just make sure they do the wheels last, and always finish with a real chamois leather (but they'd know to do that anyway, if they're good! )
There was a recent thread about this over in the Gen 4 forum (What towels, soaps, etc. you guys use when washing your car?), where I learned that I've been washing my car wrong my entire driving life Post #2 had some links with a lot more detail. I'd always heard that you should never take your Prius through a pull-through car wash (where you drive two wheels onto a conveyor and leave the car in neutral as the conveyor pulls you through), and just recently learned the reason (here). Since the traction battery doesn't charge in neutral, you would just need to make sure your battery has enough charge/is healthy enough to last through the car wash.
Detailing Your Vehicle | PriusChat The link to ToyotaNation is worth a read if you're new to detailing a vehicle. The user "Pb" is quite detailed in his/her write up. Keep scrolling as he's broken it up into sections (washing, drying, claybar, waxing etc).
Sure you can go thru an automatic pull-through car wash. As posted elsewhere, as long as your traction battery is not down it its last two bars you should have no problem. It only takes about 1 minute to go thru it. During the Winter months, I take mine thru to get the salt off and undercarriage washed. However, like most other posters, I prefer to hand wash it myself. See this thread My new Prius scares the crap out of me (ignore the title context LOL) starting with post #44, there is a great debate on car washing.
