Should you? Huh?
If they're bad questions / wrong answers, then yes.
Otherwise... maybe. Hopefully somebody was nice enough to leave a comment. If they did, you should be able to understand why people downvoted you and decide whether you can improve the question/answer, or whether you should just delete it.
Oh, and you get the Peer Pressure badge for deleting, so if you like badges, then go for it.
I usually will delete a post if I later figure out I completely misunderstood the question.
If my solution just isn't correct then I like to leave it as a "what-not-to-do" and mark it as CW so I don't lose any more rep. I think it's unfair to edit my completely wrong suggestion to basically just copy off of the one that has upvotes.
Also, for questions they usually get closed and if they continue getting downvotes, then I mark it as CW if I think someone else will stumble upon it. If it's closed as subjective or something like that though, I'll usually delete it