What would prevent you from donating blood?

Any disease which is transmittable through blood, such as hepatitis or HIV. That includes things like the flu or bacterial infections.

Any recent (within a year) piercings with non-sterile instruments or sharing of needles (such as in the case of a diabetic who injects insulin--obviously if you are on illegal injectable drugs you should not be donating blood). If the instruments were sterile, or if you are the only person to use your insulin needles, you're fine to donate.

Pregnancy or recent childbirth, as there may be danger to the mother or baby.

Small physical size--if you are a small person, your blood volume is lower and it may not be safe for you to lose a whole pint of blood. (I found this out the hard way when my doctor took less than that for blood tests and I ended up passing out on her floor. I now have doctor's orders not to donate.)

Low iron levels, again because it may not be safe for you to lose that much blood.

There are other reasons, such as suspicion of mad cow disease or malaria, but those are the main ones you're likely to run into. There is also a minimum age, usually 17 or 18.