I've always been fascinated that Paul didn't identify his thorn. A lot of people love to identify their thorns. Sometimes, in the case of addictions and groups like Alcoholics Anonymous, this is essential. In other cases, we want to wallow in the sin. Bill Clinton's sexual history was critical information. People were fascinated by the idea that George W. Bush may have taken cocaine during his college career.
Paul's goal was to glorify God. It glorified God for Paul to talk about his trip to heaven (either through a vision or a bodily translation), but it gave more glory for him to speak about it in the third person. Paul describing that God has given him the thorn glorifies God, and helps other believers to deal with their own thorns. Since the details of his thorn won't help us as much, and doesn't bring glory to God, Paul leaves them out.
We need to keep this in mind in talking about our troubles too. We are not our thorns. If God is calling you into a specific ministry (like Alcoholics Anonymous), then you need to talk about your thorns. For the "rest of us", we may need to bring less attention to our problems, and focus more about giving glory to God.
You see, I have whined here before about my weight. I've mentioned how I have trouble reading my Bible regularly. I have other thorns that I have not mentioned. I too have asked God to remove my thorns, but He has chosen to leave them with me. Spiritually, they attack me by making me think of myself as a pincushion for my thorns instead of being a child of God who still is flawed but is under grace. The Lord appears to be leading me against dwelling on my thorns, so instead of focusing on them, I'm going to accept that He will fix them when He is ready, and will strive to get past them with His grace.