To be honest I think you are confusing 'cropping' and 'resizing'.
Cropping really is cutting the edges (or more) of an image to get the composition just right. When cropping you may want to stick to a specific ratio (out of most SLRs it is 2x3 ratio), such as 2x3, 7x5, square or a pano. You will also crop slightly if trying to straighten an image to get the horizon straight for example.
Once you get the composition as you want via a crop you then need to think about the size of the image. As Trev says above resizing to say 800 pixels longest edge, 72dpi, before upload to Flickr, Photobucket, TP etc will hopefully deter image theft. For printing you may want a bigger image size and higher DPI, depending on the size of the print...