I have always been one of those developers who like to "write my own stuff" because nothing produced by another person could ever be as good as mine! I'm sure the majority of developers out there feel the same way. But as they say with experience comes wisdom and I have come to realise that maybe the solution you are trying to solve has been solved by someone else and the cost of implementing your own solution is far greater than the cost of implementing something that has already been developed and in most cases battle tested. Now there are exceptions to this but I think that, and this is especially true for Javascript frameworks, you are better off using what's been built before and which has a proven track record.
I believe that using a Javascript framework is quite important in the current web development environment. These frameworks provide rich functions that allow developers to quickly and efficiently accomplish tasks that are quite difficult and/or tedious without them. The first time I looked at the source code for the Prototype JS library (http://prototypejs.org) I fell in love. Sam Stephenson is a god and has produced the most beautiful javascript code ever! I know that what he has done in the framework simply brings together a lot of pieces that have been scattered about the development community, but that library is simply AWESOME. There are a lot of people out there who will say it is too fat and overkill for most things which is the reason frameworks such as jQuery (http://jQuery.com), mooTools (http://mootools.net), dojo (http://dojotoolkit.org), Ext (http://extjs.com) and Adobe's Spry Framework (http://labs.adobe.com/technologies/spry/) have appeared.
I personally use Prototype and jQuery in most projects, I love both of them. Prototype has, in my opinion much more flexibility but jQuery is really excellent as well and has many, many super features. I think all developers should seriously lookat these frameworks if you haven't yet, even if it's just to look at the source code and learn some excellent tricks!
