Yes, a lot. They can be considered an interesting meta-game inside this beautiful hobby.
I didn´t really care during my first months with an Xbox 360. Eventually, I befriended a group of guys who reunited in a local videogame store and were heavily invested into both Halo LAN tournaments and gamerscore races / rankings. I ultimately found TrueAchievements and other people who took this matter extremely seriously (going to extremes like not launching a game they were interested in because they knew it was hard to 100%). A significant portion of my closest XBL friends are also into achievements, so there´s a constant feedback and the occasional friendly competition.
I am no completionist, but I am probably among Argentina´s top 5 / top 10 gamerscore (317k, at the moment). I try for this not to affect my economy or my schedule, as I am also permanently invested in other aspects of gaming (Forza semi-competitive racing, Destiny, Warframe, etc.).