I'm confused about the structural formula of carbon monoxide. I was taught that carbon always needed to have four bonds, so now I'm confused ... I might sound clueless, but I didn't even know there was such a thing as a triple covalent bond.

 

Wikipedia shows the structural formula with three bonds: http://en.wikipedia.org/wiki/Carbon_monoxide

 

I'm assuming I misunderstood my teacher when I thought he said it always had 4 ... But my question is, wouldn't CO be really unstable if it had only three covalent bonds?

Carbon doesn't always have four bonds. It's capable of having four bonds and remaining stable, which is helpful, but it can be stable with less as long as it still has a full outer shell of electrons.

But with only three electrons being shared, how can an atom that had 4 valence electrons have a full 8-electron shell ??

It's not three electrons being shared, it's six, and the carbon atom has a lone pair to itself as well. The electrons in the bond are fully shared between both atoms (although one may be more electronegative).

CO is a little bit strange in it`s bonding, it has a Coordinate bond and 2 "normal" bonds, it`s called Dative bonding.

But with only three electrons being shared, how can an atom that had 4 valence electrons have a full 8-electron shell ??

 

From the octet rule point if you want its because the total electrons between the atoms is equal to 8, and in bonding such get shared in a way to satisfy the octet rule in which each atom has eight electrons via combination of the individual four atoms when the atoms were separate. This means when you use this rule you look to try and bond individual atoms that can equal to each atom in the compound having eight electrons. It gets more complicated and such is a generalization somewhat. I mean you would not say the atom became a cation to satisfy the octet rule, and other tools have been made I think.