In the writings of J.R.R. Tolkien, and in most adaptations thereof, Orc blood is described or shown as black in color.
Human blood is bright red when oxygenated, and darker red when depleted.* (This is why arteries are brighter than veins.) The red color is due to red blood cells, which are largely hemoglobin by weight if we don't count water.
The blood of other animals (and that of people with scary diseases) covers essentially the entire rainbow, with blue, greenish, purple, etc. In spiders, for instance, the haemolymph, an analogue for blood in invertebrates, is bluish because it contains a protein that itself contains copper atoms.
*If your blood is not one of those two colors, please see a doctor quickly. Just to make sure.
So why is Orc blood black? It may contain comparatively high concentrations of boron, which in its "normal" state is blackish. Boron is an important nutrient for many plants, and may have roles in human health as well.
Alternately, Orc blood may be tainted by the evil of Morgoth somehow. Perhaps the fallen god's corruption of Arda may have subtle side effects, like some sort of weird solution that appears in his servants' blood.
Heck, maybe Orcs bleed a mixture of human-like blood and crude oil—brings a whole new meaning to "no blood for oil". (An Internet search for "blood crude oil level of 20%" seems to turn up nothing especially relevant. Get on this, science!)
UPDATE: I asked "The Tolkien Legendarium" on Quora for other possibilities.
Orcs being originally harmed by sunlight would reasonably have a pigment in the blood to block penetration of sunlight; thus allowing an orcs to briefly survive exposure. Mixed with the red from haemoglobin, it need only reflect red poorly to make the blood very dark.
Human perceptions are influenced a lot by expectation. Therefore, being very dark might be perceived as “black”. —Trenton Twining
This sounds reasonable, though it does seem clear from the books that even Orcs' skin is harmed by sunlight, thus making pigmented blood of more limited use.
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