Just to make the point, the juice in red meat is not blood. It's a mixture of water in the tissue with proteins from the muscle and happen to be red because red meat (vs white meat) contains proteins similar to hemoglobin. [Extra pedant edit: Ok, all muscle contains the proteins; "red" meat just has more] But it's not actually blood.
The correct answer (in the form of a question of course) is "What is myoglobin?".
The concern that one is eating blood or somehow taking an extra risk if your steak isn't "done enough" is silly
. As mentioned in that link, beef does not contain the same internal bacteria that is found in chicken and pork. Thus, the only danger is something that is transferred *to* the cut of meat itself while its being handled. That's why it's always a good idea to cook the outside enough to kill any bugs (or if eating raw, carefully prepare the portion to remove any parts that may have been externally exposed prior to you handling it yourself). It's also why you should always brown ground beef completely (cause it's ground, so it's *all* surface if you think about it).
Preferring medium or well as a matter of taste is up to the individual, but there really are specific cuts and preparations that work well with medium/well (typically involving tenderizing and/or marinating and having other stuff than just the meat involved), but if you're ordering a ribeye or strip steak
well done, you are basically wasting your money. The cuts intended for steak have a level of natural tenderness and flavor that is designed for less than medium doneness. There are other cuts and other preparations which you should order if you like your meat cooked more than medium, but most of them aren't considered "steak" in a strict sense.
That's just my opinion of course! Edited, Sep 27th 2012 2:03pm by gbaji