Will a 32 bit intel app run on Mountain Lion? I have Lion, running on a 64 bit kernel 

$ uname -a
Darwin dyn1158-144.insecure.ic.ac.uk 11.4.0 Darwin Kernel Version 11.4.0: Mon Apr  9 19:32:15 PDT 2012; root:xnu-1699.26.8~1/RELEASE_X86_64 x86_64


but I have a number of 32 bit apps (among which, to my surprise, Google Chrome) that run perfectly fine.

I am not overly concerned about Chrome, but there are a few things I'd loathe to lose, either because they cost me money (Photoshop CS3, which should actually work), or because I like then (Luna menu, RapidoSerial, which are not on RoaringApps).

Is there a final yes/no answer to the question, will a generic 32 bit intel app run on ML?
For a generic 32bit Application the answer is yes, confirmed yourself with Google Chrome. it should run just fine.

Now for Utility programs, and programs that interact directly with OS X specific features, the answer will likely be no, those programs will need updates to run at their best. 

Applications interacting with hardware, will also likely need updates or tweeks to their drivers in order to work.

Other than that you should not have to worry about running 32bit programs on Mountain Lion. I would try checking the developer's websites for Mountain lion compatibility to be sure on your expensive mission critical apps before upgrading full time to Mountain Lion.