I realized after penning it that this answer is really similar to Shmuel Brin's. I'm posting it anyway just for a fuller explanation, and one relevant to the main-site post that led to this question.
The pun in the main-site question referred to above was as follows. The question was about plants that grew in a filled-in hole. Now a bor is, in halachic terminology, anything that can be tripped over or into which animals can fall: it's a term from tort law, nothing to do with plants or the question asked. When the question indicated that the hole in the ground had been filled, it added, as a pun and in parentheses, "bor no more". To set up that pun, the previous paragraph was:
A neighbour of mine, had a fire hydrant replaced in front of the house, right at the curb, and the fill used settled leaving a hole. (Is that a bor? Does that make him responsible halachically?).
To me, that last parenthetical remark is distracting from the question (which, recall, was about the plants that later grew in the refilled hole). Moreover, it might have encouraged users to address that question instead of the actual question being asked. That's why I removed it, and I still think I was correct to do so.
So IMO whether puns should be removed depends on the puns and their effect on the question. Putting "bor no more" in a question about a bor is IMO certainly good; putting it in a question about plants that grew in a former bor is IMO okay (the distracting-ness is minimal because it's only three words and in parentheses, and a pun is worth including); but putting it in a question about plants and setting it up with a long parenthetical remark off the topic of the question is IMO no good. Likewise, inclusion of humor in general is fine if it fits in to the question, not if it distracts the reader therefrom.