Man, I'm going to feel like the old guy here. I've had plenty, all on PC though. I've never been very good at console shooters but I'm getting better (There actually was a time when I was great, back in the N64 days of Goldeneye, but I started playing PC around the same time and I lost my way with the controler). Anyways...
The one's that stand out the most. Almost getting 100 kills (I was in the 90's) and no deaths during a Call of Duty: United Offensive, CTF match.
Delta Force: Black Hawk Down, I went 30 kills a few times without dying. Though I can't remember if getting a medic stopped me from recieving a death.
Battlefield: Vietnam, Had many games with kills in the 20's and no deaths.
Lasty, Planetside...yes I played it, but damn it was fun at the time. Now I don't remmeber if there was any kind of stat page to view but I remember at times and even during the games peak, I would spend hours on the same life on multiple days. And I would get anywhere between 15-50 kills. Depending on where I was, who was with me and how many "bad guys" were out there.
