The "Dynamic Text" effect allows you to overlay a timecode - which counts up relative to the start of the clip or timeline it is applied to.
Hint: You can add effects to entire video tracks by clicking on the Track Header and chosing Timeline>Add Effect. Video tracks that have effects added to them are marked with a yellow star in the Track Header . If you add this effect to the Video track rather than individual clips the timecode will not reset at the begining of the next clip but rather count accross the whole length of your project.
See also the Render Overlay option in the render dialog to add time code or frame count to the entire rendered project.