However hard you try to stay still, you will sway from side-to-side, or from front-to-back. A sturdy tripod, set on solid ground, will allow exposure times of several minutes without any camera shake.
The main risk of movement with your camera on a tripod is the moment you press the shutter button to start the exposure. Touching the camera can introduce a slight shake. This can take a second or two to settle down and might affect exposures of a few seconds or more.
To avoid this you can use the built-in self-timer on your EOS. This allows any movements introduced as you press the shutter button to die away before the exposure is made. The 2-second delay is ideal when photographing static subjects with your camera on a tripod.
Ray of hope, © Marco Lieberwirth 2010, Canon EOS 400D
If you are photographing a moving subject and need to fire the shutter at a precise moment, you can use a Canon Remote Switch. The switch has a short cable with a plug that connects to the remote socket of the camera. At the other end of the cable is a small unit with a button. Pressing the button fires the camera without the risk of moving the camera.
Lion at night, © Pierre Morlon 2010, Canon EOS 400D
Many EOS cameras offer a mirror lock-up feature, set using a Custom Function. The reflex mirror inside the camera reflects light up to the viewfinder. At the start of an exposure, the mirror swings up to let the light through to the sensor at the back of the camera. However, small vibrations can be introduced in the camera as the mirror hits the foam dampers at the top of its rapid travel.
With mirror lock-up, pressing the shutter button once raises the mirror. You can then wait a second or two for the vibrations to die away before pressing the shutter button again to fire the shutter.