Not if done properly. Although executed with appreciable energy, a good, clean fencing attack hurts no more than a tap on the shoulder. The force of the blow is normally absorbed by the flex of the blade. Reckless and overly aggressive fencers can occasionally deliver painful blows, however. Fencing *is* a martial art, so you should expect minor bruises and welts every now and again. They are rarely intentional. The most painful blows tend to come from inexperienced fencers who have not yet acquired the feel of the weapon.
The primary source of injury in fencing is from pulled muscles and joints. Proper warm-up and stretching before fencing will minimize these occurences.
There is a risk of being injured by broken weapons. The shards of a snapped blade can be very sharp and cause serious injury, especially if the fencer doesn't immediately realize his blade is broken, and continues fencing. Always wear proper protective gear to reduce this risk. FIE homologated jackets, britches, and masks are ideal, as they are made with puncture-resistant fabrics such as kevlar. If you cannot afford such extravagances, use a plastron (half-jacket worn beneath the regular fencing jacket), and avoid old and rusty masks. Always wear a glove that covers the cuff, to prevent blades from running up the sleeve.
Fencing is often said to be safer than golf. Whether or not this is true, it is an extraordinarily safe sport considering its heritage and nature.
The best training for fencing is fencing. Fencing development is asymmetrical and few other sports use the same muscle groups, so this is a difficult question whose answer depends largely on what aspect of your training you really want to focus on.
The answer is clear - foil. Or is it sabre? Would I be incorrect if I said epee? No, it's foil - if you fence another weapon you're just a wanker who couldn't cut it.
Such a question is an open invitation to religious warfare. Everybody loves to participate, but nothing is ever settled.
Different people mean different things by "real" fencing.
For some, "real" fencing is a duel with sharp swords and lives on the line. Other than the fear/courage factor, the primary technical difference here is that with live blades you only need to hit your opponent once, and therefore only require one good move (which explains the prevalence of "secret thrusts" in the bad old days). The sport fencer, by comparison, has to hit his opponent as many as 15 times (even more if the officiating is poor!), and so requires considerably more depth than the duellist. On the other hand, the sport fencer takes many more defensive risks, since he has up to 15 lives to work with.
The Olympic sport of fencing is comprised of three weapons: foil, epee, and sabre. All are fenced on a long rectangular strip, and electronic scoring aids are normally used to assist in the detection of touches.