The only one of these games that I played was League of Legends, and even then, that was quite a while ago (in fact, I started playing when it first came out). I never ended up venturing outside of LoL because, well, the others weren't out yet at the time, and by the time they were, the friends I was playing with were obsessed with LoL - and playing these games without people you know is, usually, not as great an experience.
But, truth be told, I was never a great fan of these types of games - and both my net and computer kind of suck, and so did my playing ability (totally because of the pc and net, not my own fault in any way).

dota2 is most popular from these games, and it is awesome. But the problems are:
1. you may start hating people if you play without your team
2. too many crazy russians who play realy bad and scream all the time
Well, for the second "problem" at least, LoL had several servers set up (three if I remember correctly: Western Europe, Eastern Europe, and North America), which could help mitigate any "cultural shock" - it also had a "mute" button.

Don't the other games have something similar in place?