I've certainly placed restrictions on myself before which usually led to me becoming a better player.
In TFC I became really good at sniping from a distance and started getting bored so I stopped using the zoom. Eventually I had become better than I was before because I was still getting headshots, but now I had a much better field of vision. In fact, I'd regularly take out other snipers in little sniper duels without zooming which was kind of funny. When that got old I started attacking as a sniper instead, which also worked quite well since I didn't need to zoom. When TF2 came out I actually couldn't adjust to playing sniper because I was so used to playing without zooming and running into the thick of battle. Not surprisingly, when the Huntsman was released I took to it quite quickly.
And in most other multiplayer FPS I tend to play like I have a death wish because I get bored easily. I rarely stop moving and often charge straight at enemy players. It's lead to developing some pretty impressive shooting skills over time, as well as developing a strong ability to read the way the battle is going and change direction quickly so I can get around opponents or mess with their ability to aim at me (one of the interesting things about playing sniper a lot in TFC and TF2 is that you get really good at predicting other peoples movements making it easier to survive things you shouldn't simply by moving unpredictably. I've actually dodged sniper and other bullets quite successfully in a lot of games by changing direction at the last possible second).
There's also Turok 2. Back in the day I was quite a bit better than everyone I played against so I gradually restricted myself on weapons. First I only used the assault rifle and crossbow, then later just the crossbow. It was interesting because I had to go for headshots to kill someone since they were using rockets, cerebral bores, etc. Unfortunately this backfired because I got very good at headshotting anyone with the crossbow as soon as they entered the screen, and I can't remember ever missing twice in a row. Not long after that people stopped playing with me.
In other games I may often just dick around, but not usually as seriously as those times. Like in CS, I'll often use a scout and try not zooming quite a bit. It's actually not as bad as it sounds once you get a feel for it.