You just want to cut off part of a layer - not crop your whole document?
Hit C for the crop tool - that will crop the WHOLE document.
If you just want to crop parts of a layer down - you can draw a rectangle selection (M) around what you DON'T want and hit delete - or - a better way - draw a rectangle selection around what you DO want and hit the 'Add Layer Mask' button at the bottom of your layers pallette.
This doesn't erase anything - just hides it. It's a great technique.
one way to do this would be to draw a marquee around the area of the layer you want to keep intact. then click the "add layer mask" at the bottom of the layers palette.
you can leave it like this if you think you're going to want to change it later. if you're absolutely sure you want to ditch the other parts of the layer then right-click on the layer mask button (in the layers palette) and select "apply layer mask. the other parts of the layer will now be gone for good.