There are many reasons why people like them. Many like it because it is highly customizable and people can play around with them, others like it because of its high (perceived high) CDI (Chicks Dig it) factor, and then others like it because it is rugged and relatively reliable when left in or nearly stock form and used with quality ammo and a good maintenance protocol. Others like it because of its high magazine capacity relative to other commerical rifle offerings.
Unlike commercial rifles (hunting type rifles) the AR-15 is drop safe. Hunting type guns are not. This means you can carry it in the Action or Ready mode instead of Transport Mode. commercial rifles are not safe when there is a round in the chamber and they're suddenly dropped. The AR is built to be abused by young men/women nervous their first time in combat and about ready to fast rope into a hot LZ and the rifle accidentally falls 25' to the ground.
As a factory certified AR-15 Armorer working on these for the past 20+ years, I see a lot of these rifles (literally 100s + per year) and I can say based upon my experience those that are highly customized and upgraded to "match this and match that" and/or have poorer quality ammo are more prone to breakage and reliability issues. This is a general statement. Not ALL of them are in this category and there exceptions to this general rule. Those who take good care of there factory stock or near stock carbines and run good ammo in them and take a competent persons advice on maintenance will find they are extremely reliable.
I'm certain there are people on here who know more than me, have more experience than me, and are smarter than me. So, I'm fully prepared to be challenged on what I know and my experiences. I can say like many things in life there are those who highly polarized and biased...some lov 'em and some loath them.
Is the AR the best rifle for you? Depends upon your needs. I say, find out what you need a rifle for...how and what are you going to use it for, then let the mission dictate the gear. Don't buy an AR because it has a perceived high CDI factor or because you can ad a bunch of crap to it you don't need. Buy what will fulfill your need (or wants).