These are pointers to either Commercial or Free tools for audio recording and editing. Note that most companies offer both "full" and "limited edition" versions of their products -- the LE versions are typically much cheaper. Also, many companies offer very good discounts on their software for educational use. This list is broken down by Mac and Windows versions of audio software.
For the PC
Adobe Audition used to be Cool Edit Pro. Very nice, full featured audio editing application, priced accordingly.
Sound Forge another very full featured, powerful audio editor, but XP is almost as powerful, and costs a lot less. They offer educational pricing.
Goldwave is a quite powerful audio editor for the money. The interface is a little busy though.
Audacity -- Very capable open source audio editor available for many platforms that is free.
Hard Disk Ogg -- A simple, free audio recorder for Windows that can record into compressed audio formats such as mp3 or ogg-vorbis.
WavePad is another free, basic audio editor for the Windows Platform.
Total Recorder is an inexpensive application that can record audio from applications running on your computer (i.e. streaming audio).
For the Mac
Audacity -- Very capable open source audio editor available for many platforms.
Ardour -- Open Source audio workstation software, similar to ProTools. The software requires that you have the X11 host software installed (in developer tools on your Mac OS X installation CD) and Jack, a system resource that allows audio to be re-routed from one application to another. Set up is not terribly difficult, but it does require a bit more work than simply clicking on an icon.
Bias sells several audio applications. Peak is a classic 2 track audio editor, Deck is a multitrack audio recording/mastering application. Soap is a very good noise reduction package available in a "Pro" and "Regular" edition. The non-pro version is very handy for removing ambient noise in video footage, noise from vinyl LP's, etc. Note that Bias offers educational pricing on their software.
Amadeus II is an inexpensive audio editor that has a nice feature set and is stable. The author has a very flexible demo system -- it counts number of times you run it, not number of days you have it installed.
DSP Quattro is a professional audio editing application that has features similar to Spark, an audio editor that is sorely missed by some (i.e. me). It is not particularly cheap, but it's quite fast and feature-rich.
Audio Recorder is a dumb audio recording application this is free, and can record directly to mp3. It's not an editor, but it's very useful for recording interviews, etc.
ProTools is an industry standard tool for audio recording/mastering that Digidesign gives away for free. It takes a some time to master, but is quite powerful. PC users need to read system requirements carefully as it only works with certain sound cards. There is not a free version of ProTools for Mac OS X, only 9.
Audio HiJack is a audio recorder that allows you to record from audio inputs, and also from any program that is playing back audio (i.e. streaming audio). The Pro version includes support for VST hosting, so you can add realtime audio modification plugins to your recorded content. Very handy indeed.