This video advocates turning off VSync. There are some important disadvantages (and advantages) to doing this however.

Advantages:
1. You MAY get smoother gameplay, IF (and only if!) you were previously capped at a lower FPS than your screen's refresh rate in Hertz.
2. Latency may be reduced by a very small amount, although for most people this will not be noticeable.

Disadvantages:
1. Screen tearing will become evident, as your GPU pushes frames to your screen faster (or slower) than it can display them - resulting in "half-frames" being rendered and the tearing effect. For some people this is more annoying than having lower FPS, but everyone is different.
2. Your PC will use a lot more power, and generate more heat and by extension noise. Because by un-capping FPS, your system then uses all its resources to render as many frames as it possibly can.

Summary/tl;dr:
You should aim to cap your FPS at the same rate as your screen's refresh rate. For most people this will be 60FPS/60Hz, though a few high end "3D" screens support 120Hz. If your screen's refresh rate is 60Hz, then it is impossible to increase your visible FPS beyond 60 (despite what the numbers say), except by buying a new 120Hz screen!
VSync should do all this automatically for you, and triple-buffering should be enabled as an extra defense against screen tearing. This will ensure the smoothest gameplay possible with no tearing. If you do this and find that latency/lag has noticeably increased, then look to reduce your latency in other ways: such as not using wireless keyboard/mouse and using ethernet instead of wi-fi. Bluetooth keyboards and mice are particularly bad for gaming latency-wise.