The only multiplayer military shooter I play is
Red Orchestra: Ostfront 41-45. That has no single-player campaign at all. One side takes the part of the Germans, the other takes the part of the Soviets, and they fight until one side wins.
I enjoy this game for a number of reasons. First, I like the Eastern-Front setting and weapons, and the attention to historical detail in general. Second, I enjoy its comparative verisimiltude: death comes easily, and tactics and teamwork are rewarded. Third, it also rewards skill and practice: the most common weapon is a bolt-action rifle, which is not at all easy to use, especially without crosshairs. Fourth, there is (or at least was) an active modding community, producing both new maps and full-conversion mods like
Darkest Hour, which covers the campaign in northwest Europe in 44-45.
As for the general appeal of such games--in my opinion, they're really no different from any other competitive team sport. They have a playing field, and two teams, and rules, like RL games: they're just played online, instead of IRL. In that sense, playing
Red Orchestra is no different from playing softball, and has much the same appeal, especially if you join a clan and take part in competitive play, as I have.
The puerile behaviour of many online gamers just comes with the territory. In my opinion, it's a problem with the internet in general, rather than online gaming in particular. When there are no consequences for rude and vulgar and antisocial behaviour, many people--especially young males--will choose to be rude and vulgar and antisocial, the same way they do in an online discussion forum.
In some ways, I have found the RO community to be better-behaved than some others, in part because it seems to attract a somewhat older and more serious-minded type of player. I've certainly never encountered the sort of behaviour that is quite common in, say, the Left 4 Dead community when playing RO. But on the down side, the chance to play the Germans on the Eastern Front attracts a small number of racists and neo-nazis and SS-lovers. Luckily, they're not all that common, and are banned from many servers which have rules against racist usernames or remarks.
I guess, overall, this type of online competitive play either appeals to you, or it doesn't. If it appeals to you, you have to put up with a certain amount of assholery and douchebaggery. If it doesn't, you don't.
Personally, I'm looking forward to the release of
Red Orchestra: Heroes of Stalingrad in the near future.
