I ask a question and lo and behold, I discover, thanks to others, it's already been asked and answered. Is it best for me to simply delete my duplicate question, or does it somehow serve a purpose (beyond embarrassing me)?
I would say to just leave it, as (and this is just one reason) it could be used as a statistic to help find "canonical" questions. In other words, if a question has been referenced many times by duplicated questions, it might be considered canonical.
There might be ways to query this information out of the Stack Exchange Data Explorer, e.g. Most Commonly targeted dupes, which indicates that the question How to Start Web Mapping? is the most duplicated question on the main site.
There is one more reason why you shouldn't delete your new question. You might have phrased the question or problem differently than the original question. Maybe you phrased it in simple and non-technical terms.
In the future some beginner might have a similar question and wouldn't know what keywords to search for. So he might use a non-technicial term in Google Search, which would lead him to your question, and in turn to the original question.
If you delete your question, this hypothetical future noob, will not find anything on our site; certainly not the original question.
That's why I don't delete my new question, even if a duplicate is found. (I also vote to close it as duplicate, but that's a different discussion)