I run a lot (20-25 miles per week) and the other day when I began my run, my knees started to hurt. After the first mile, the feeling went away. Is this something I need to worry about?

As long as the pain went away and did not return, it probably is nothing to worry about.  You might want to think about what may have been different about the run that could have caused pain to occur:  new shoes, unusual terrain, poor warm-up, etc.  If you can identify a factor, avoid it in the future.

If pain increases with subsequent runs, it is important to avoid trying to "run through" the pain.  Instead, you should seek help from a physician who has knowledge about running injuries.