There are many proteins that transport oxygen in the terrestrial biosphere, this, and this.
One thing to note is that at human body temperature, atmospheric pressure, and Earth's atmospheric concentration of oxygen Hemoglobin is by far the most efficient oxygen transport protein among the list included in this post. It varies from 50% more efficient to 10x more efficient than the other oxygen transport molecules listed here.

Hemoglobin uses iron as its metal atom. We are all familiar with hemoglobin and its color red.
Hemocyanin's can be found in certain mollusks. It is colorless when not transporting oxygen and blue when transporting oxygen. Hemocyanin uses 2 copper atoms in its protein structure and the protein is very similar (but not identical) to hemoglobin.
Chlorocruorin's uses $Fe^{II}$ as its metal ion.
A dichromatic compound, chlorocruorin is noted for appearing green in
dilute solutions, though it appears light red when found in
concentrated solutions.
Hemerythrin uses $Fe^{II}$
Hemerythrin is an iron bearing oxygen transport protein often found in
the muscles of marine invertebrates.
Hemerythrin and myohemerythrin are essentially colorless when
deoxygenated, but turn a violet-pink in the oxygenated state.
Erythrocruorin is an iron bearing protein. I didn't find definitive description of its color but I think it would be a light red.
Erythrocruorin is a large oxygen-carrying protein, whose molecular
mass is greater than 3.5 million Daltons. It is related to the similar
chlorocruorin. It is found in many annelids and arthropods (including
some insects).
and Earthworms.
Pinnaglobin
Only seen in the mollusc Pinna squamosa. Brown manganese-based
porphyrin [oxygen transport] protein.
Coboglobin is currently a synthetic protein that performs the same function as hemoglobin. It uses Cobalt in place of the iron atoms.
Blood of this type would be amber yellow in color when in the veins
while uncoloured and clear in the arteries.
It might make an interesting blood for synthetic biological organisms (like the one found in the movie Aliens)...
Chloro-carbonyl-bis(tri phenylphosphine)-iridium
An Iridium (one of the Platinum Group Metals) ion based molecule that is yellow when oxygenated and dull orange when not. It provides the additional capability of serving as a hydrogen transport molecule too - which might make for interesting biology on a gas giant planet. The organism would require a biological/chemical pathway to generate oxygen from chemicals found in the environment and then transport that molecule to the cells that needed energy. Perhaps the oxygen circulatory system and hydrogen circulatory system would need to be separated?
In solution, the compound takes up one atom of oxygen per molecule to
change from brilliant yellow to sullen orange...
In the oxygenated condition, the iridium-based blood of
extraterrestrials would have to be protected from light because it is
very photosensitive. The pigment slowly decomposes over a period of
days or weeks when exposed to strong light, gradually changing color
from orange to green and finally to a deep bluish-black. Such aliens
would therefore either have very dark skin, or would inhabit a dimly
lit world. (In the absence of light, the molecule is stable for
years.)
The iridium complex has one additional property which is extremely
fascinating to xenobiologists. In addition to oxygen, the molecule is
also capable of reversibly binding hydrogen as well!
In Summary
- Pink (Iron - Hemerythrin)
- Red (Iron - many)
- Orange (Iridium - chloro-carbonyl-bis(tri phenylphosphine)-iridium)
- Yellow (Cobalt - Coboglobin, Iridium - chloro-carbonyl-bis(tri phenylphosphine)-iridium)
- Green (Iron - Chlorocruorin)
- Blue (Copper - Hemocyanin)
- Violet (Iron - Hemerythrin)
- Clear (Cobalt - Coboglobin, Iron - Hemerythrin)
- Brown (Manganese - Pinnaglobin)
All but two of these (the exceptions are the Cobalt and Iridium based molecules) are known to exist in living organism in the terrestrial biosphere.