In Unix, can I run 'make' in a directory without cd'ing to that directory first?

make -C /path/to/dir

As noted in other answers, make(1) has a -C option for this; several commands have similar options (e.g. tar). It is useful to note that for other commands which lack such options the following can be used:

(cd /dir/path && command-to-run)

This runs the command in a sub-shell which first has its working directory changed (while leaving the working directory of the parent shell alone). Here && is used instead of ; to catch error cases where the directory can not be changed.

If the reason you don't want to cd to a directory is because you need to stay in the current directory for a later task, you can use pushd and popd:

pushd ProjectDir ; make ; popd

That goes into the ProjectDir, runs make, and goes back to where you were.