In my opinion the main 4.
Zend
http://framework.zend.com/ is the big and popular one, the chaps that build it also build the Zend engine that runs PHP now days (from 4 onwards) so they know what they're talking about. It's also pretty widely used in commercial environments if you're planning on applying your skills in the direction and you can do also sorts of wildly recognised qualifications to do with it.
Symfony -
http://en.wikipedia.org/wiki/Symfony Another big one, used on several large sites, very versatile and comes with lots of features already included, loads of developer aids and JS libraries. Very much a large scale framework for larger sites and competitor to Zend.
CodeIgniter -
http://codeigniter.com/ My personal favourite. Not as comprehensive as Zend but plenty powerful enough, a damn site quicker to learn, plenty of add-ons and unlike other frameworks doesn't come with a stupid console you have to use. Dubs itself as the lightweight framework which it is but don't take that to mean underpowered take it to mean quick, it's also developed by a company so it's always polished and well supported. Found in professional environments as well and would be recommendation.
CakePHP -
http://cakephp.org/ Very similar to CodeIgniter except done by a load of individuals rather than a company. Has a console for quick scaffolding if you like that sort of thing. Would say it's not quite as wildly used in commercial environment as CI and on a personal note I've never liked how they lay their documentation out, I find it hard to work with.
Personally I'd start on CodeIgniter for any sort of smaller project (by small I mean not an international website, not a 4 page static site) and build a CMS with it or something, then once comfortable with that move on to Zend.
PS Once you know your way round CodeIgniter, don't bother building a new admin each time just use
http://cibonfire.com/ a pre-built shell.