jQuery's selectors are unique. If you cannot let go of them, you should stick to this lib.
However if you still want to change, here are some interesting options:
Other frameworks
jQuery is far from being the only JS framework out there. Actually, with its weird "$" object and the funky selectors, jQuery is arguably the least javascript-y framework available.
Why not try something else? Some of the examples I know:
You can safely expect coverage for a vast range of browsers be provided in most of these frameworks.
Make sure to pick one that provides canvas support, and you're in for hours of graphics drawing fun.
Front-end framework
That's the new trendy thing. Frameworks that are more than simply a few JS libraries. They usually provide templates for HTML, CSS, a directory structure and JS extensions. Of course cross browser compatibility is taken into account.
Here are the two most interesting:
Their main advantage is the native support for mobile systems.
Superset languages
If all you're looking for is to write some JS but you're not the biggest fan of the syntax, there are some efforts to develop new languages to
replace it. These languages usually compile to JavaScript and therefore should run on every browser natively (no need to ask your users to install any weird plugins - we already learned that mistake from Silverlight).
Unfortunately, I feel that these languages are primarily aimed at programmers with strong JavaScript skills looking to simplify their programs. Someone not familiar with JS might have a hard time debugging.
In any case it doesn't hurt to check these out:
CoffeeScript is the closest to JS (it's "just JS", and they make a big deal about it). Dart and TypeScript focus on giving JS the features necessary to manage very large applications, mainly static (optional in the case of Dart) typing and class-based Object Orientation. TypeScript has the advantage of being backwards compatible, meaning any existing JS code is de facto valid TypeScript code. Or so they claim.
Keep in mind that these projects are at their infancy and should be handled with care.
JavaScript, the Good Way
Finally, nothing prevents you from rolling up your sleeves and getting your hands dirty in plain JavaScript. From the experience I have with the language, it's not a newbie-friendly language. Not because it's difficult to understand, you can write your apps quickly, but because the language does very little to prevent the programmer from writing bad code.
The language is often described as a "toy" language, although in my opinion it's more powerful than what enterprise developers might tell you. It does have some flaws, like the adoption of C-like syntax (the language is a lot more similar to Scheme or Lua) or the partial support for prototypal OO designs.
If you decide to write your own JavaScript, I strongly suggest reading
JavaScript the Good Parts by Douglas Crockford. The book expects some familiarity with programming in general, and focuses on the subset of features that make the language powerful (the Good Parts), while carefully avoiding the harmful features (the Bad Parts). The same author has written
JSLint a static code analyser (it's a tool that analyses your code without executing it) that helps you get rid of the Bad Parts from your code. It also plays very well with Continuous Integration servers like Hudson.