Classical and chamber music lends itself well to a "pastoral feel" in a dive video. A co-worker that does some very nice videos uses a lot of Classical, and when I put together a short video of our last dive trip to Mexico, I asked my flute teacher for permission to use a track from her ensemble's CD.
Himalaya Bay, October 2009
Some issues to keep in mind: While many compositions, particularly classical or folk music, have been around long enough to be "public domain" on copyrights, the actual recordings are often still protected works. Some artists have no problem with people using them for applications such as this, as they basically consider it free advertising, but others are very protective and will have websites such as Youtube block the audio portion of the video. The more contemporary the composition and/or recording, the more likely you'll deal with copyright infringement issues.
Using the "Jaws" theme for shark footage is so overdone that it's annoying. I started watching one dive video on Youtube this weekend, and didn't make it even half-way through before I went and found another that didn't play the "doon-doont, doon-doont-doon-doont-doon-doont..."
Whatever music you use, IMNSHO it's simply good courtesy to the artists and the viewers to credit the song and performer. If you know a webpage for the artists, include that in the credits.