Finding a good Windows client was easy. TortoiseSVN is an Explorer shell extension that is free, stable, and complete. It worked right out of the box with Google Code and I didn't have to read a single line of documentation to become proficient at it.
The situation wasn't quite as simple for Mac. There are multiple non-free clients for Mac, but I wanted to stick with open source if possible. The closest thing to TortoiseSVN for Mac is something called SCPlugin, but it is incomplete and development on it seems to have stalled in 2005 or 2006.
SvnX is the one I ended up choosing. It is not quite as intuitive as TortoiseSVN, but it seems to get the job done. To get it working with Google Code, I had to run this command on the command line in order to accept the security certificate:
svn list https://GOOGLE_CODE_CHECKOUT_URLThat's it! Off to do some programming.