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