I'm not sure shadowing a doc really counts as an EC, but it is a very good idea and can always help during an interview.
I shadowed two docs. One I got hooked up with my calling my private HS's alumni office and asking - turns out the head of the alumni association's brother is a doc. The other doc I shadowed spoke to a pre-med symposium my college put on. I met him, talked about his field (colorectal surgery) since my research involved intestinal stuff. Then the next week I called him, re-introduced myself, and asked him if I could shadow him during January (when my college doesn't have classes). It sounds hard to do, but after you've done it you see how really easy it is.
I think the more difficult question is WHO to shadow - what kind of doc (male, female, old, young, etc), specialty, type of practice, location, etc etc.