Obviously it depends on many things.
As a general rule, use em for anything which is text-related, and px for anything which is decoration-related. So padding and borders should be px, text size, widths, heights, etc. should be em or % (or better yet, fluid layout).
Just imagine you're using large text display; what elements would you want to be bigger? Making the borders bigger is likely to leave less space for the text, so would really be a negative thing.
For line-height, you should use no units (or em, but that's a waste of 2 characters); it is a proportion of the font size. If you used px, you could end up with a line-height which is smaller than the text, which is bad.
This site raises an interesting point about unitless vs. em: http://meyerweb.com/eric/thoughts/2006/02/08/unitless-line-heights/. The idea is that using em will set a fixed line-height for all children, even if the font size is different, whereas using no unit will use a line-height which is always relative to the font size. In most cases the latter would be preferable, but I can think of situations where you would want the former too.