I don't know anyone who plays things like quake from work to internet servers, maybe they play in the office out of business hours, but not normally across the internet.
ROFL...Each of the huge corporates I've worked at has always had people playing Quake1/2/3 online. People tended to especially enjoy being LPB's courtesy of a fast corporate net connection. One multinational headquartered in the UK where I worked used to suffer ethernet meltdown on Friday afternoons due to a combination of game traffic and porn-surfing (when the email servers broke one Thursday, and weren't fixed until the start of the next week, an email was sent round saying that of the X thousand emails stuck in the queue for the past five days, something like 60% were non-business-related, and 20% could result in being fired according to the standard employment contract!).
Typically the game-playing is carefully moderated by the employees themselves - half an hour of quake during a lunch break every now and then gets tolerated, especially when people are arriving in work at 6:30am each morning. I've spotted even the most moralistic of employees doing it at some point or other

. I even have a friend who was somewhat embarrassed to be caught by his boss playing Quake *and* Solitaire at the same time

.
More general TCP v.s. UDP conversations should be directed at that long long thread over in the networking topics.
Um. We appear to be in the Networking topic?

. Anyway, I've made the TCP/UDP thread sticky, which should hopefully minimize accidentally going over the same ground!
But in terms of firewalls, from behind a corprate firewall as I commented and jeff confirmed, the most likely option is port 80 for client outgoing traffic, and UDP is the least likely.
...and which of course has led to the thriving business in HTTP-tunnelling options in various modern apps

, and the existence of articles with titles like "How to tunnel ANYTHING via HTTP". Chuckle.