After students learn to use it, they'll love it.
This is the best audio editing tool I've used. There's some complexity to it, and it takes a while to download and install it on each computer, but students like it once they learn to use it. My only other complaint is that between the current version and the previous version, some of the controls got moved around so we had to teach students how to find the new controls. This has only happened once, though, over the course of two years.
How I Use It
The most important project we do with Audacity is a podcasting project. Students research a historically significant musician, create a brief essay about the musician, and record the essay as an MP3. Then, students select one or two songs the musician made and weave the songs into the MP3. The resulting product is an audio piece where the listener hears the musician's work and the student's commentary woven together artfully. Audacity lets students adjust the volume of their voice (we recommend amplifying to 2 db) and the volume of the song. It also lets students cut and paste sections of any audio track (Audacity calls this making "split cuts") so that students can align their spoken commentary either with important moments in the musical track or with quiet parts in the musical track. Editing recordings of their own audio essays helps students improve their writing and their public speaking skills. Editing the musical tracks helps students learn the ins and outs of musical phrasing. Audacity plays a key role in both of these.
We also use Audacity for smaller projects. When students went on a field trip, for instance, they recorded some audio reflections about what they learned, edited the audio with Audacity, and then paired it with a slideshow of photos from the trip.
Small tip: We find that students often press the "pause" button in Audacity when they should be pressing the "stop" button. Many editing features are not available when the track is paused rather than fully stopped.