First of all, if you record yourself practicing and then listen to the recording, you're practically "double dipping" in your practice time. It's the best possible way for you to improve on your own... everyone is their own worst critic, and we can hear our own flaws much easier when we're not worried about playing the darn thing. In preparation for auditions, I always record EVERYTHING, and then listen to it later. Hugely helpful, and puts the "improvement factor" on steroids. Extend this to teaching, and the same thing happens. Students hear the mistakes they're making (or the "stuff" that I keep harping on as their teacher) and realize what needs to be done to fix it. I also sometimes ask them to record their practicing so I can help them develop appropriate practice habits and help them use their practice time efficiently. It's always incredible how many students practice like crazy, but accomplish nothing because they don't know HOW to practice. Getting students to listen to their playing (when they're not busy actually playing the piece/etude/excerpt/etc) is key to their continued development. It gets them analyzing and critiquing their own performance, and it also starts them on the way to self-improvement without the constant need for a teacher. With my more advanced students, we play orchestral excerpts and then compare their recordings to mine, or their recordings to those from a professional orchestra, or mine to a professional orchestra. It's amazing what the students are able to hear, and then incorporate into their own playing. When one of my students has an audition on the horizon, I'll put together a "mock audition" for them and record it, so that they can listen back on their own time. Also, when dealing with a large ensemble rehearsal situation, I often record the rehearsal so I can listen back later, analyze what I didn't hear on the podium, and take steps to fix it up at the next rehearsal. To accomplish all these recording tasks, I use a (oh... free advertising) Zoom H2 series recorder. The thing is awesome... you can record anything in beautiful quality sound. It has two sets of xy microphones, allowing you to record in stereo... fantastic. You can also listen to yourself through the device as it has a playback feature, and supports SD cards up to 8GB in size. If you're a musician, or a teacher, buy one. Seriously.
The second thing I use, much in the same way as the Zoom recorder, is a Flip video recorder. It's small, easy to use, and you can easily watch the videos on the machine. Furthermore, it's very simple to hook it up to your computer, and watch the videos on a bigger screen, email them to students, etc. Same principle here as with the audio recorder, but it allows the students to SEE their hands, and then correct the problems they see. I've also used it when teaching students crash cymbals, as they can SEE how they're crashing, and correct any technical deficiencies. The Flip recorder connects directly to your computer, no cord needed, allowing you to quickly and efficiently watch the videos/save them for future lessons, etc. It should also be noted that Zoom just came out with a camera similar to the Flip recorder, that uses the same microphone set up as found in the H2 audio recorder. Might be worth checking out.
I love it when technology not only improves my own practicing and rehearsal efficiency, but also helps my students to improve as well. Seems to me this is the whole point of technology - it works, it's useful, and it allows us to do things never before possible. It's user friendly, not at all clumsy or cumbersome, and really does fulfill a purpose that would otherwise remain unrealistic.