Beat mixing is definitely a cornerstone DJ skill that all DJ's must possess (the sync button doesn't count). But, like all rules, it is meant to be bent and sometimes even broken.
Mixing adds that smooth transition between two similar tracks. Not only can a DJ mix using the tempo, but also, a DJ can mix key's, melodies, instrumentation and music styles. All of these come into consideration before the DJ switches over the song.
But there are times when mixing isn't going to bring energy into the room, when mixing will be too slick for the style of music.
In hip-hop, often times mixing in a song half tempo can really get people moving or in reverse, double the tempo.
Even further out there is echoing out the song that doesn't match tempo, but matches keys or style. This technique simply can't be performed by a robot or iPod correctly, so it is a skill I use to add the energy only a skilled human DJ can bring.
Finally, there is mixing (or in this case not mixing) with your voice or even silence. Sometimes giving a little gap of no music and add the thrill of bringing the music back!
Play it Cool,