The use and implementation of recordings have always been a controversial issue in music circles, since the technology in a lot of ways had managed to revolutionize people's conceptions of the musical experience in itself. During the Romantic and late-Romantic eras (~19th century), music establishments began to facilitate the "genius" narrative into its cultural discourse, emphasizing the "vision" and enlightened ideals of the composer over the expression of the performer. As a result, notational practices became more specific as to tailor the music towards the composer's subjective experiences and perspectives.
The invention and implementation of the recording, however, allowed music to be abstracted in a completely different way, turning Romanticism up on its head. The technology allowed music to be "captured" into a fixed form, after the fact, as opposed to notational practices in which the abstraction exists a priori. Popular, folk, and jazz musics partially owe its success (at least in terms of its commercial and influential value) to recordings, because it was largely the technology that enabled those styles of musics to disseminate into the public sphere.
With that in mind, as an improvisor I think that it is important to recognize the fact that the recording medium is largely used for two purposes -- as means of capturing a musical event, while at the same time providing a vehicle to broadcast it beyond its original context. The question of whether or not musicians should be recording their improvisations is something people have been asking themselves ever since the invention of the phonograph, and now that access to cheap and reliable recording equipment is fairly commonplace the issue has become something that musicians face on a fairly regular basis. Broadly speaking, within the world of improvisation there seems to be three main attitudes toward the recording medium:
1) Purists - Opposed to recordings on any level, arguing that performances should be live and live only. The defiant attitude against the technology usually stems from political reasons, arguing that recordings distort and filter out too many things from the live experience, as well as commodify the event in such a way that makes it vulnerable to political appropriation.
2) Documentors - Are willing to record their sessions, but with minimal or no edits. Tries to maintain the objectivity of the event as much as possible by treating the microphone as an outside observer/listener.
3) Editors/Composers - Are completely willing to edit, process, and alter the recorded material after the fact. This approach is much closer to the act of composition compared to the other two, and includes musicians such as DJs and laptop performers who use process-oriented tasks as their primary means of achieving variation.
These categories tend to be hyperboles, however, and it's rare (especially nowadays) to find people who would strongly identify themselves as being part of one of these "camps". In reality, most improvisors tend to use each approach methodically according to circumstance, although some may find themselves more comfortable doing one thing or the other as a matter of personal preference.
"Pure" improvisation tends to be good for pedagogical situations or playing with someone for the first time -- this relieves the pressure of having to "produce" something and allows the musicians to perform privately amongst themselves. The musicians can then focus more on communication, listening, and developing a relationship with the other performers rather than worry about the product that might come out of the process.
The "documentational" approach is useful for reviewing and reflecting on the sessions that had been recorded. Good or bad, how a musician "feels" after a jam session can sometimes be deceptive when compared to the actual result -- this helps to ground the experience into something tangible, so that it can be viewed from a different perspective. Many musicians have used self-recording as a way to gauge their skills and identify areas in their performances of where they might be able to improve upon.
The "editing" approach tends to find itself most often used in electronic music, where recorded samples are used as building blocks for creating larger-scale pieces. It is also used heavily in film and video productions, where improvised musics are used to "fill-in" certain durations of time, or in other cases, used as material for the mixer's whim. Samples can also be used as a basis for composed works, which seems to be gaining a lot of traction in the electronic music world at this point.
For better or worse, the presence of the recording device tends to do something to a person's state of mind, and it's fairly remarkable how drastically some musicians' playing styles change with the knowledge that they're in the midst of being recorded. It's kind of like being looked under an aural microscope, where your every move is being monitored and recorded, which can greatly increase anxiety levels for many performers.
In order to get more comfortable with the idea, it may help to remember that the recording medium is a fairly new technology and Western society has not yet developed proper "methods" of how to behave in front of a microphone as of yet. So there aren't any real "rules", per se, although there are certain physicalities that the musician has to consider if they're looking to get a clean, commercially viable recording. But if that's not really the intension of the session -- say, if you were only recording something to get a general idea of where your current skills lie -- then it doesn't really make sense to spend a great deal of time worring about the gritty details of how the recording might sound post-production.
The relationship between the musician and the recording medium can vary wildly according to the needs and long-term goals of the performer. Thinking about these things in advance can help the improvisor make intelligent decisions as to how to deal with the microphone during their performance sessions and hopefully be comfortable with it in its place. A string quartet playing something by Bartok might treat the microphone as an outside observer, while a rock band might use amplification and processing in order to vary the captured sound in itself. Ideally, if a recording device is being used, the musician should be comfortable enough with it that it becomes part of the performance itself. More details will be written about this on a later post.