I wish to programmatically determine whether a solaris system is 32-bit or 64-bit. Investigation on the web suggested that the following commands were the right way to test this:

# isainfo -kv

# getconf LONG_BIT

Strangely, on all three of the solaris systems I have access to, isainfo returned
64-bit sparcv9 kernel modules
but getconf returned 32! Which is right? I had believed based on statements by a former coworker that one system was 32 bit and another was 64 (and I didn't know for the third), but then when I went to check, I got really confused.

A "solaris system" is a collection of things. You need to specify exactly what you want to measure. " isainfo -kv" is telling you that you have a 64 bit kernel. "getconf LONG_BIT" is an odd command to run. It is telling you that as the getconf program was being compiled, a "long" integer would have been allocated 32 bits. Here's why:
They are both right and do not conflict.

Another thing to try is

getconf -v POSIX_V6_LP64_OFF64 LONG_BIT

or

getconf -v XBS5_LP64_OFF64 LONG_BIT

The -v option specifies a 64 bit environment. I don't think the getconf command is returning 32 just because it was compiled as a 32 bit executable. I believe it is returning 32 because your default compiling environment is 32 bit. It should be getting its info from /usr/include/limits.h or /usr/include/unistd.h

I don't have access to a solaris machine, so I cannot test this out for you.