Why?
Because they look dangerous?
I believe that either is the main reason or has a lot to do with it. Resemblance to the M-16, which is seen in all contemporary war movies imparts a certain macho mystique to it.
I'm a relic from the M-1 Garand era, which was one hell of a weapon. Big and heavy, but it will take out an adversary right through a cinder block wall at 500 yards. But the present ideal is light weight and Buck Rogers imagery.
I've never seen an AR-15, which closely resembles the M-16 and probably accounts for its popularity. Based on all I've read and heard about both weapons my preference inclines to the AK-47, which is very sturdy, extremely reliable -- even in wet, sandy conditions, and is relatively simple to disassemble and clean. Plus a good AK-47 is priced at around $400, while an AR-15 costs $1,500. I don't know how much an M-16 costs but it must be around $2,000.
I'll be interested in hearing from those who have hands-on knowledge of all three of these weapons. Which is the better weapon, and why?