Just a note really, as it may help explain the issue of tearing.
High FPS from the game probably won't cause graphical anomalies (where anomalies are things like odd colours, strange artifacts, objects and textures that are clearly not right, stuff like that). Though some old games are reliant on frames per sec as a measure of speed in the game and very high FPS can cause them (or parts of them) to run too fast. I played Colin Mcrae Rally 2005 and its framerate was very high. It didn't really affect the gameplay but the animations of the driver and navigator in the vehicle was too fast and their heads were just shaking up and down very fast. Vsync fixed this.
What a high FPS in game will cause is graphical tearing. In a first person game this is more easily seen when you are close to a wall texture and you turn quickly. What you see is a very momentary split in the image, but it only lasts a fraction of a second. Slow movement won't make the tearing visible as there isn't much change in the image.
What causes this then? Well, if your GPU is churning away through frame after frame at a high rate then this will give you a high FPS as it keeps asking for more and more information to generate the display (because newer hardware is capable of more calculations and more storage than older hardware). However, your LCD monitor only has a refresh rate of 60Hz, so no matter how fast your GPU is creating the frames to be displayed, your screen can only show 60 every second. So, when you are generating a great deal more frames than your monitor can display, what happens is the monitor gets only some of the frames to be displayed, and when there is a big change in the display it can sometimes show part of one frame and part of another causing the tear in the image.
What vsync then does is to restrict the GPUs ability to process the frames so that it only handles the same refresh rate as the monitor so that the monitor gets ALL of the frames generated for the display and thus preventing tearing. However, vsync does cause a load on the GPU which may lower its performance whilst the vsync is in use, but modern hardware shouldn't have any issues with this.
There is also frame buffering. Commonly there is double buffering, storing one frame for processing whilst displaying the other. If you have a bit more beefy hardware then you can up it to triple buffering, storing two frames for processing whilst displaying the other.
Some games suffer graphical tearing more than others, some it is more noticeable in than in others, and some you can just live with. For example, I recently played through Serious Sam: First Encounter (from GOG). Vsync doesn't work in it, though, and forcing it through the drivers just makes the game jumpy, so I had to live with it. However, it was only really noticeable with the big tower like scenery in the large arenas but the game is too fast to really notice it anyway. They fixed vsync in Second Encounter, though, and you can tell the difference.