A couple of years ago I rented a Suzuki jeep for about one week from a car rental company outside Phuket airport. I didn't have to leave my passport with the car rental company, they made a photocopy. Now I hear from many sources that you can no longer rent motorcycles in Thailand without leaving your passport in the company's safe.
Does this apply to car rentals too? Obviously I can't leave my passport with the rental company for a week as I'll need it to check into hotels, also for doing banking and other business.

i did not need to leave my passport for my rental in phuket last year, nor did they make a copy as i remember...they did take down the number...

You should 'never' leave your passport and it certainly would never be required by any registered decent rental business at all, Avis and Budget both have places at the airport, 2 others are David's Car Rental and also Airport Car Rent, sorry don't have the websites, do a search on Yahoo. ( except Budget which is www.budget.co.th )
Don't forget you need an International DL/Permit, rental companies don't ask but it's the law !!

I worded that badly, you need your passport to rent but certainly don't need to leave it!

Texas, here's Airport Car rent, I normaly drive down but once or twice when flown have used, nice cars, I would avoud the Suzuki Jeeps as they really are not that comfortable, you are better off mith a compact sedan. Otherwise when else I stick with Budget as they have lots of locations.

http://www.airportcarrent.com/

Tip, if you are going May to October ask them what they can offer for about B 1,000 ( that temps them to offer a deal, there will naturally be a lot of cars lying around low season so worth bargaining for even if it comes out a little more ), but around B 1,200 would be normal.

Many thanks James & Bob. I agree you should never leave your passport as security, the Aust Em firmly advise against this practise but nonetheless, I got howled off the other forum about a month ago over this.
I recall Best car Rent charged me about 600Bt a day to rent a Suzi in 2003. I've emailed them for current rates (also asked about the passport)
I also usually drive my own car but will be coming back in after 8 months down under, so will need to find another car to buy.
It's just great to rent right at the airport and be mobile instantly, also don't have to deal with the taxi/songteaw mafia.
I'll be getting to Phuket about April 22, so I think the things are starting to slow down by then.