Depends on the role but for full time references are nearly always done and they typically want supervisory references. For contract roles the recruiter will often ask and contact. References are a good test to see if you’re actually being looked at hard. If they ask for references but your references don’t get contacted, often something is up.
Richie’s points are very important and I think necessary to get you a positive reference. You want them to match what you’ve said are your strengths and it could be worth giving what you feel is an improvement area. I think that could get you tripped up in a reference check.
I recall it recommended to do a QA on your references, having someone contact them to review what they say. I think that may have been an outplacement thing, CC maybe you can weigh in if that’s something you’ve seen recruiters do on behalf of the job searcher?
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