If you spend a great deal of time working with PHP in your development process, it makes sense to consider utilising an established framework for a number of reasons - namely, writing your code faster and more cleanly. However when it comes down to actually choosing a framework, opinions are wildly varied; fans of some frameworks almost reach the point of religious zeal when it comes down to one choice over another. For those of you just starting out with frameworks, this can create an overwhelming and conflicting set of opinions, so let's take a step back and discuss a few basic considerations about what you hope to achieve with your framework.
The primary concern about selecting a framework is to ensure that it has an active community behind it, as that's what creates the strength of a framework. Frameworks let you quickly and easily reuse code for many common functions and situations, letting you focus on the areas of your application that are specific to your situation. As you can guess, this means that the more people use and contribute to a framework, the more robust and useful it will be.
When you build an application using a framework, your code is inherently dependent on the security and stability of the entire framework codebase, so it can be critical to stay on top of any potential exploits or vulnerabilities that are discovered, and an active community can make this much easier.
The next most important consideration is the quality of documentation within the framework. We've all spent many a wasted hours trying to understand another programmer's undocumented code, and with a framework the problem can be 10 times worse. Typically, most frameworks have decent documentation, but it's worth exploring to see which documentation you find easiest to understand and work with. What clicks for some coders won't work for others, so be sure to check this out.
Finally, if you're looking for a framework to help you out with a small, single project, you might want to reconsider - frameworks can often add a great deal of complexity (not to mention execution time), which can make them unwieldy for smaller one-off applications. Even still, however, they can offer you some excellent reusable code that might make things simpler, and if you plan on doing a good deal of PHP coding, then learning a framework early on can save you hours of hassle and reinventing the wheel.
Now that you've understood the basic considerations of framework selection, visit Wikipedia's comparison of the various PHP frameworks here and choose one that you're comfortable with. The best framework in the world isn't any use if it you don't enjoy making use of it!