From an Adobe FAQ regarding support for Snow Leopard (http://blogs.adobe.com/jnack/files/Adobe-SnowLeopard_FAQ.pdf).
Q. Will older versions of Adobe creative software—such as Adobe Creative Suite 3 or Macromedia® Studio 8
software—support Mac OS X Snow Leopard (v10.6)?

A. Older versions of Adobe creative software were not included in our testing efforts. While older Adobe and
Macromedia applications may install and run on Mac OS X Snow Leopard (v10.6), they were designed, tested,
and released to the public several years before this new operating system became available. You may therefore
experience a variety of installation, stability, and reliability issues for which there is no resolution. Older versions
of our creative software will not be updated to support Mac OS X Snow Leopard (v10.6).

Q. Are Adobe® Creative Suite® 4 products and components compatible with Mac OS X Snow Leopard (v10.6)?
A. Yes. Working closely with Apple, Adobe has tested and determined that our Adobe Creative Suite 4
products and components are compatible with Mac OS X Snow Leopard.

From an Adobe FAQ regarding support for Snow Leopard (http://blogs.adobe.com/jnack/files/Adobe-SnowLeopard_FAQ.pdf).

To be fair, this was later issued:

John Nack on Adobe: Information about Photoshop CS3 on Snow Leopard (http://blogs.adobe.com/jnack/2009/08/pscs3_on_snowleopard.html)

Essentially, the team apparently did do some testing of CS3 on Snow Leopard and found it to have reasonably worked. This was subsequently supported by a few other early independent (non-Adobe, non-Apple) Snow Leopard reviews published recently.

As for a partial list of known apps with Snow Leopard issues:

Snow Leopard - what doesn't work ? The Register (http://www.theregister.co.uk/2009/08/27/snow_leopard_incompatibilities/)

As of this writing no plugins that utilize Quartz Composer will work with After Effects CS3 or 4 in Snow Leopard. This includes any 3rd party plugins that requires FxFactory (http://www.noiseindustries.com/). Adobe has acknowledged the bug and we can presume they are working on it.
After Effects and Snow Leopard - Keyframes (http://blogs.adobe.com/keyframes/2009/08/after_effects_and_snow_leopard.html)

BTW, FxFactory plugins work fine with Snow Leopard and Final Cut Studio.