I've previously discussed the possibility of freezing in space, so let's look at another common space based theme. Does your blood boil in space? The idea here comes from the boiling temperature of liquids. Water on Earth boils at a temperature of 100 C. Water on Mars, however, boils at a much lower temperature since the air pressure pushing on the water is much lower. This makes it easier for individual water molecules to quickly escape the water (boiling).
Air pressure is extremely low in Earth's atmosphere so it makes sense liquids would boil very quickly, and this is true. However, the blood in your body is part of a closed system with its own internal pressure, so the blood in your veins/arteries would NOT boil. Liquid exposed to the air, however, would boil. Saliva on your tongue will boil off as will any sweat on your body and liquid on your eyeballs. This is not a good thing, but much different from the blood in your body boiling.
To conclude, it's never a good idea to remove your suit in space, but if you did, your blood would NOT boil.