The DPI and overall sensitivity I use is considerably lower than that of most people in this thread. I use a DPI of 450. With a windows sensitivity of 6/11. In FPS, my ingame sensitivity tends to be very low. In Counter Strike:Global Offensive, it is 1.75. In something like battlefield 4 it is as low as 3%.
I know it sounds horrible to a lot of people. And even for me, this kind of sensitivity was once silly. Many years ago, when Counter Strike 1.6 was really popular as a competitive game, I kind of ran into a wall. Despite the hours I put in, I felt unable to improve past a certain point. At first, I focused on the metagame to try and improve, and sure enough, this did lead to me being more successful in the game. But the simple fact remained that my speed and accuracy was not what I wanted it to be.
So after using a fairly high sensitivity for years (most people would think of it as a medium sensitivity). I one day decide to use a lower sensitivity. Even though it is silly to mimic the style of play of a pro gamer, my main reason for trying this out was that my favorite players at the time all had a low sensitivity playing style. Of course, because a certain level of sensitivity works for someone else does not mean that it works for you. However, I forced myself to stick with a lower sensitivity for a week or so.
During this time, I did not do matches with the people I normally play with, but just stuck to doing whatever helped me get used to the new sensitivity. Which at first meant playing a lot of Team Death Match. After just as little as a week (though playing every evening of every day during that week), I found that my overall accuracy and speed had already increased compared to my previous sensitivity that I had been using for years in other games (and for about a year and a half in CS 1.6).
Me and the guys I play with sometimes have LAN ( about twice a year ), and people always think it is fun to watch me play due to my sensitivity settings. These days, my sensitivity is lower than the one I copied from my old heroes. I tried to find a video to kind of show what that looks like. I found this, and I can tell this is almost the exact same sensitivity I play with:
t=2m20s
Here is another, from a well-known player. Though not quite as clear as the previous video:
I chose these videos because they show both the mouse movement and what happens on the screen. What you can see with those videos, is the kind of trade off that you get with using a low sensitivity in FPS. Yes, acquiring a target can be a lot easier for some people at low sensitivity, but you have to be able to do constant rapid sweeps of the mouse or your response would be too slow. Additionally, things like turning 180 degrees, will always be slower with a low sensitivity compared to a high sensitivity. That is why a low sensitivity might be more useful in some games than in others, depending on the accuracy needed, and the overall speed of the game.
Anyway, this is all just from an FPS perspective.
This playstyle is also what sparked my interest in mice (see the guide in my signature). Playing with a very low sensitivity is quite demanding, and exposes many problems a mouse may have. The problem that is most common is that sensors simply do not track at the speed with which you move the mouse. This practically forces you to go for gaming mice with decent sensors. Also other issues, such as acceleration may just be a theoretical problems for some, but if you swipe the mouse over large distances all the time, it becomes quite noticeable.