The really sensible comments here are those from Gail and Jeff (that's pretty much as usual).

I've usually limited myself to things like emailing my personal email address to friends (friends who were colleagues and had only my company email address), wishing individuals well, and other purely social (as opposed to professional) things.

Once I did it a little differently. In 1975 when I decided to leave ICL (I'd had 45 great months with them, but the next three months had been utterly depressing) I talked to the divisional director (VP in USA-speak) in a local bar, and said "I don't like the ivory tower you've transferred me into, and I don't think I can cope with the guy who runs it, so I've started looking for a new job - are you willing to provide reference if needed?"; the result was that I stayed with the company for another 21 years

.

I found over the years that I quite often ended up using a company I used to work for as a supplier of something or as a customer for something, or being recruited by people who worked with me (or worked for me, or that I worked for) at former employers, or recruiting them. So it would probably be a bad idea to send some goodbye that would lose potential friends.