UPDATE: My improved script for a minimal PHP 5.3.x install with mysqlnd and APC is now available on Dreamhost's wiki.
With shell access to the server, you're free to compile your own copy of PHP. Then, with a couple of lines in an .htaccess file under your site's root, you can be up and running with the latest - and greatest - version of PHP.
The only caveat: Dreamhost will not provide technical support if you go down this route. (That's unlikely to concern you, however, if you're willing to build your own copy of PHP.)
Whilst this may not be the most optimal arrangement, it's great if you can't afford - or don't really need - a VPS, and just want something to tide you over until other hosts adopt PHP 5.3 - and there's choice in the marketplace.
It's been only a few days since I started setting-up my web space, so I'm not in any position to comment on performance and the like. For what Dreamhost are charging, though, I reckon you'd be hard-pressed to complain.
Compiling PHP 5.3
There are basic instructions and an install script for PHP 5.3 on Dreamhost's wiki.
In the interests of saving time, I started-out using their script. PHP failed to build on the first run-through, however, so I've just started stripping-down the script and altering it for my own purposes. When I'm done, I'll post the script and instructions on the wiki for reference.