Many of us tend to think of Deer as docile subjects, which they usually are, just don't go near a loser during the rut! A friend of mine had to "leg it" a bit sharpish when photographing a Red Stag. He was using an APSH camera (1D4) and a 400mm lens, so he was certainly not close but had to dive for thick bushes, where the deer's antlers were too large to enter, so he could escape! The deer made quite a mess of the Rhododendron bushes that he dived into! When sneaking up on some Red Deer I found myself being stalked by a Pere David Buck - he got annoyed with me from 300+ yards away! Another Pere David simply went for me just for the hell of it! Luckily I was setting up an Archery target so I had something to hide behind.
Note these were all "Park" deer who are VERY accustomed to having people/dogs around - sometimes they just get grumpy..............