jQuery is pretty good at providing changelog and compatibility/migration tools. If you read up about what changed in the major revisions you should be fine before updating. There will be sections of your code which need to change but not significantly.
You'll want to do a full regression test on any core javascript functionality in your applications. Sometimes third party plugins or scripts need updates as well.
Needing to support old versions of Internet Explorer is one thing which might prevent the update.
The key benefits to updating are smaller library size, much better performance, and new techniques + functionality.