I myself am 14, so consider that I might be a bit biased in this instance.
I feel that it does not depend nearly as much on age as it does on maturity. For example, staying civil-tongued on Xbox LIVE, sticking with a team, and playing smartly. High pitched voices do not bother me much unless they're extremely loud, have tantrums, etc.
I got Left 4 Dead right around when it came out (for 360), and I feel that in most games I played online, I was a valuable addition to the team-the people I played with were for the most part respectful, and it was fun. I stopped playing for a couple months, and when I came back to it, I got put in a match where there was what sounded like a 7 year old, who would just run off, get hit by a tank and incapacitated, then whined incessantly for someone to revive him. This is the only issue with age I have.
What really bothers me is how on some sites, the majority of people think that children and teenagers should be banned from all games, because they're stereotypically immature. I don't think age is a very good thing to base game choice off of, I think maturity plays a much larger role.
EDIT: Oh yes, the desensitization thing. Video games don't desensitize kids, the WORLD does. On the news, it's always murder, violent theft, and some country bombing some other country. In my 8th grade language arts (I'm technically a high school freshman, just finished 8th grade) we did whole units on slavery and the Holocaust. People attack video games for desensitizing kids, but when it's in a classroom it's suddenly just "oh it's education, kids need to know this stuff." So we get to the point where we have teenagers seeing all this violent history in school, when games like 6 Days in Fallujah get dropped by publishers for being too "controversial" when they are also about (much more recent) history which people ought to know about.