First, please don't confuse POLARITY with PHASE. The (mislabeled for goofy reasons) "phase" button is really a polarity reverse button. It's flips the polarity.
Among other reasons, the two most common reasons to use this button are:
1) When working with live signals with multiple mics, if things aren't mic'd well, you can get phase problems. Sometimes the phase is convenientaly close to the point where one signal is a half cycle away from it's related signal, in which case hitting the "phase" button (which is really a polarity reverse button!) will get you closer to a good sound. This is mainly only an issue with very complicated micing schemes like live drums.
2) Some sounds will sound different, plain and simple. There are two categories: transient and tone. Transient things like kicks are a big issue and you want the initial transient to push the speaker forward as opposed to backwards. It makes a subtle difference. With tone, things can go horribly wrong. Certain vowel sounds and many brass instruments have more of a sawtooth wave shape and flipping the polarity will drastically affect the tone. If the track was recorded with polarity reversed (miswired cable, for example, or the wrong side of a figure 8), then you can correct it with the magic button.
And of course, in hip-hop when you have things like layered kicks if they have opposite polarity it will sound more squishy than punchy. Common problem. I catch this kind of crap all the time when I mix records.