Lots of reasons. Firstly, everyone likes rooting for the underdog. They are the underdog (some would say) in this situation, Intel is far larger. AMD also has alot of fanboys, people who would sell their kid before admitting AMD is wrong.
AMD is usually (on the desktop market) cheaper than the equivalent Intel. And some lower AMD processors have been known to higher end Intel (famous one was the Duron and the Celeron, where much lowr Duron's outperformed higher Celeron)
AMD has the feature of (usually) leaving their chips able to be unlocked easily. This appeals to overclockers and enthusiasts.
Lastly, AMD chips usually run hotter than Intel, which is another reason why they are cheaper.