A couple of definitions of the word "Improvisation", straight from the internet dictionaries.

Improvisation: the act of making or doing something with whatever is available at the time:

Improvisation: a performance that an actor, musician, etc. has not practised or planned:

Improvisation: the art or act of improvising, or of composing, uttering, executing, or arranging anything without previous preparation:

Improvisation: Something that is improvised, in particular a piece of music, drama, etc. created spontaneously or without preparation.

We improvise constantly. Every day dialogues are not scripted. They evolve from a topic and the language skill of the participants. Adapting to events of the day is improv. We do these things well because we have language skills and survival instincts. Music can be utilized similarly if you study its properties.
SA

"Real improvisation happens when the unpredictable meets the unexpected."
—Greg Howard

We play an instrument that is perfectly suited for real improvisation, in harmony, rhythm and texture, the three dimension I like to ponder when improvising. Explore at least one dimension all the time when you are improvising. If you are not, then you are probably not improvising at all, you are just rehashing things you've done before.

I recommend a simple book on improvisation for you to check out:

Free Play by Stephen Nachmanovitch...

http://www.freeplay.com/2-main-writing.php

[youtube]http://www.youtube.com/watch?v=6ZfgG8B0Y3Q[/youtube]

It's amazing how this word, "improvisation", can be interpreted according to the situation. When we listen to a musician who improvises well, we feel that he has control of his instrument. When a government, a football team or any other similar situation makes a mistake, it is said that he or she has improvised. Fascinating.

[youtube]http://www.youtube.com/watch?v=R3uyZFmjF40[/youtube]
[youtube]http://www.youtube.com/watch?v=WBbj_QixnL8[/youtube]

Hey, cool! Lots of really great input - thanks for all of the replies! As far as great improvising goes Miles Davis "So What" is a benchmark for modal improvisational playing in my opinion...

Anyways, this video of Mike and Leni Stern practicing really stands out to me, it's kind of where I want to go as an improviser on the Stick.

The I believe Improv.

[youtube]http://www.youtube.com/watch?v=3YIm6WGwg_4[/youtube]

Great topic!

Long story short - I still spend a lot of time doing improvisation, but it takes a fair more constrained role in my actual performance or refinement of pieces. As I'm a singer and voice coach, I have to create interesting accompaniment that supports and interplays with the voice.

As such, I explore things improvisationally during practice, but I have to refine each avenue I explore so that they become useful within song accompaniment. The accompaniment needs be interesting and I need to have many many ways/versions that each accompaniment can be played... however it can't be as loose or free as full on improv. The pieces must always come across as complete pieces that feels consistent performance to performance, even if subtleties or nuances might be different.

Hence, lots of exploration in practice, followed by hefty repetitions/refinement of successful avenues to create useful variations. This leads to more focused and less obviously improvisational performance.

And of course, for the Stick not enough mention can be given to this guy; amazing!