The games I panic in morst are Team based RTS's where I have teammates relying on my every move, which packs on the pressure. Unlike most other genres, theres is a limit to the slack a good player can take up when paired with a not so good one, meaning synergy is key. Also, in 1v1 match-ups I usually start off shaky, but after a few matches, wins and losses, I get comfortable and start to perform better. I have to go through this phase each time I boot up and RTS.
Or Dark Souls/Demons Souls when a black phantom invades, usually because I'm completely ill prepared or totally focused on something else that the FLASHING NAME startles me, causing me to enter the fight with my worst foot forward. Conversely, when I invade other players, due to me having the element of surprise I don't get as jittery, but I'm not devoid of tension either. Something about the 1v1 side of things cripples my focus. Too personal maybe.
I don't recall ever panicking in games like Left 4 Dead, mainly because I always played with mates and we never got to worked up on the goal of winning and instead just played for fun... which often resulted in winning strangely. Even as last man, I would be having a ball, with my mates cheering me and jeering me in equal parts.
Other "Team" based games like Elimination game modes or whatever game in that vein you think of, are usually stress free for me too(beyond bullshit events that we all flare up over), because more often then not, there is no TEAM element. Just one big clusterfuck.