If I install Debian stable and have "stable" in the sources.list file, will updates keep happening, even across releases? I think it would be great it I never had to reinstall, yet could still have a completely up-to-date system.
"stable" is just a pointer to the latest release. So if you put now "stable" in sources.list you'd be running Sarge. When Etch gets released, "stable" will point to Etch, so your system will upgrade (more or less) automatically next time you run apt-get update. Also if you add the security updates repository you will get critical security updates between releases.
Also, is the same true for unstable and testing?
For testing: yesFor unstable: the unstable "release" (Sid) doesn't have releases, your system will just get new packages as soon as they are available (sometimes causing major breakage :))
And yeah, it's one of the great things with debian - there is no need to reinstall it whatever happens, you can always down/up-grade it to whatever you want.