I've been using Prototype/script.aculo.us for a over a year now, and have found it pretty good. I've also just started using JQuery, and found that to be really cool, much more fun than Prototype. Please post what js framework you use and why. Thanks.
I use prototype.js. I haven't found a good reason to use anything else, yet.
prototype/scriptaculous as part of Rails.
Mootools! Definitely mootools - it's like stripped down, modified, cleaned and polished prototype. With a bit of work it can integrate with Rails nicely (using a Minus-mor), and the best part is that it encourages you to remove all the bloat from your own javascript classes, resulting in a lot cleaner code. I haven't used JQuery, but I'm hearing a lot of good things about it too, either way, prototype+scriptaculaus is just too fat for me right now (I've had pages where a "Document Size" query yielded a result of 105 K - 100K javascript + 4K html + 1K images ... that's just too much)
Mochikit. The quiet framework in the back of the room.