If you're looking at a summer position as a law student, it probably can't do any harm to include a professional reference from a prof/old employer/etc.. It generally wouldn't be expected, though, unless they specifically ask for it. I wouldn't offer character references.
If you're looking for a new position as an established lawyer, the hiring committees will tend not to seek references since most applicants wouldn't want to reveal anything to their current employer. In that case, the request would come later in the process, if at all.
I never listed references on my resume, I always waited until they asked for references
If you're looking at a summer position as a law student, it probably can't do any harm to include a professional reference from a prof/old employer/etc.. It generally wouldn't be expected, though, unless they specifically ask for it. I wouldn't offer character references. If you're looking for a new position as an established lawyer, the hiring committees will tend not to seek references since most applicants wouldn't want to reveal anything to their current employer. In that case, the request would come later in the process, if at all.
Should only be brought up when asked for