After using Skype for over a year, I'm pleasantly surprised at how well it works. The sound quality is a lot better than it used to be, and it offers some interesting advantages:
1) Recording the lessons is easy, both in audio and video. The student can later review the lesson, or practice with the recording if appropriate.
2) Zooming in on either hand is easy by moving the camera or the player around, both so the teacher can look at the student's hand, or vice-versa.
3) Re-scheduling due to traveling is reduced - students who are away can keep their regular lesson times, or find an alternate time for that week more easily.
4) Lessons are available to students who do not live in town.
5) The personal connection we expect to have in private lessons might take a little longer to set in, but after a couple of weeks things do feel great.
6) It saves travel time. A one-goutr lesson ends up taking a couple of hours out of the student's schedule. With Skype, they can take some of that time to set up, tune, and warm up before the lesson, and to immediately review the lesson right afterwards. Combine this with the lesson recording, and the process can get supercharged!
A few of the drawbacks to look out for are:
1) Avoid getting caught in the technical stuff - after you set up Skype, focus on the lesson. Some students worry about the connection quality so much they have difficulty concentrating on the playing itself.
2) That said, a good internet connection is paramount, for both parties. But once it's going, focus on the lesson.
3) There is a time lag that makes it very challenging to play together, so if that is an integral part of the lesson, you might want to have pre-recorded tracks the student can use.