The biggest impact of R 3.3.0 will be on Windows because they have updated Rtools33 to use version 4.9-3 of the mingw compilers, after having used a prerelease of 4.6-3 for many, many years. Exceptions (which are a common occurrence when running Stan programs) are handled differently in the 4.9-3 version, so I think it is impossible to use Rtools32 with R 3.3.0 or to use Rtools33 with previous versions of R. Stan is workable with R 3.3.0 and Rtools33, but that does not mean that it will work for you on Windows. We probably have failed to anticipate some issues pertaining to bitness, CYGWIN, arbitrary corporate policies, Windows versions not equal to 7, etc., so to repeat: don't upgrade unless you know what you are doing. There are revised instructions on how to use Rtools33 on
https://github.com/stan-dev/rstan/wiki/RStan-Getting-Started
When upgrading, make sure that you do not (auto) load any stanfit or stanmodel objects that were created with a previous version of Rtools into your Global Environment on startup. This is a common source of problems when you select "yes" after it asks you if you want to save your workspace before quitting R. You can avoid this by always selecting "no" (which is what I do) or by deleting the .RData file (which may be hidden) from your default working directory.