Halo pretty much made FPS online games. It's what started everything in a way.
I'd personally hand that title to Counter Strike. If I am correct, it has always had and still has the largest number of people playing it online over a decent period of time. It's also the biggest in terms of competitions. Halo kicked it off for the consoles, but the FPS online genre has been around for long before then on a large scale.
I dislike the Call of duty fanbase the most. They genuinely do seem to believe that Call of Duty is a really good game, but the thing is that the game hasn't changed one bit since Modern Warfare in my opinion, and it's only as far as there as that is the first Call of Duty game I played. Someone who wrote and article that has played all of the games made an article stating that Call of Duty is such a good game that it has been re-made 8 times, which I really don't doubt. I also remember reading a review where someone was playing Modern Warfare 3's online(let's face it, this is the only thing people really buy Call of Duty for), he said that if he hadn't read about the changes in the game play that he wouldn't have noticed them, he then went on to say that he probably would have thought that he was playing Modern Warfare 2 if he was just told to play without actually knowing what game it was. Yet the fans all still go on about how Call of Duty is such a good series. I thought that Modern Warfare was good, but since then they've just been re-skinning it and then releasing it as a new game. That isn't what makes a good game series, and I hate it when they try and argue that Call of Duty is even a good series, never mind a series which is as highly rated as it is.
Everyone will eventually get bored of doing the same routine every day.