This short summary was inspired by reading two editors complaining about the quality of scientific papers. The first is an editorial in Nature Physics that covers more than conclusions. Upon reaching that topic, it cites another writing `nearly solely' on introductions and conclusions.
They both attack the simple-minded view -- all too often sustained by examples in actual papers -- that useless conclusion only restates either the abstract or the introduction (depending on style requirement of journal). And with that I can agree. In other words, it is padding that adds nothing and was included because the author thought a conclusion was mandatory and had no idea how to write one.
They do admit that a conclusion that restates the abstract in a more sophisticated form that the intervening paper made possible would be fine. Shewchuk's formulation is excellent:
A good conclusion says things that become significant after the paper has been read. A good conclusion gives perspective to sights that haven't yet been seen at the introduction. A conclusion is about the implications of what the reader has learned.
But he goes on to say "Of course, a conclusion is also an excellent place for conjectures, wish lists and open problems."
Skilled authors can pull this off. But I would urge most to resist the temptation. The reason is simple: too often the author reach a conclusion not supported by paper. That is, the author fails to label it a conjecture, allowing the reader to think it was proved in the paper.
To answer my title: write a conclusion if you can produce one that sets your results in a broader perspective than would have been impossible at the beginning and, indeed, is only possible now because of the paper's contributions.
But, if you are giving a talk that really had a "take-home message" don't fail to clearly make this the last thing the audience hears. If you already have an excellent version of the take-home message, use it again. But if you can cast it in new way that takes advantage of ideas in the talk you have given, then let that conclusion "bell" resonate and persist with the audience.