1. Cross-browser differences with JavaScript can be largely eliminated. No need to re-code that bit of animation so it works in IE 6 as well as Firefox 3.5, jQuery will handle it all for you. Don’t get me started on the ‘for…in’ construct and how ‘.each()’ saves the day every time.
2. Everything you want to do is even more simple than you can believe. What used to take over a dozen lines of code can usually be expressed in one line.
3. Chaining. It may rile some programmers up, but when you can chain function calls together on a single object, you end up with cleaner, more readable and more semantic code.
4. Plug-ins. There are so many of them around now that just about anything you want to do has already been done at least once. Sure, the jQuery site could use some improvements when it comes to searching the docs or plugin database, but it is all there for you.
5. Light weight. In comparison to MooTools, jQuery is quite hefty. But when you compare it to nearly every other JavaScript framework out there, you will see that when minified, the library is small enough to justify its addition to your code base. Every byte transmitted and processed delays the user seeing your website, so you have to balance the good against the bad!

These are my reasons, what are yours?