Many people have seen the Classical depiction of Satan in paintings and statues, but what does scripture say about what Satan looks like?
Apparently, anything he likes, including an angel:
... Satan himself masquerades as an angel of light.
Assuming Satan is an angel, then he can probably take on any appearance, at least that of a human:
Do not forget to entertain strangers, for by so doing some people have entertained angels without knowing it.
And possibly a snake (though some Christians do not take this passage literally)
Now the serpent was more crafty than any of the wild animals the LORD God had made.
More information can be found on the Christian demonology Wikipedia article.
Don't forget the images in Revelation:
an enormous red dragon with seven heads and ten horns and seven crowns on its heads. Its tail swept a third of the stars out of the sky and flung them to the earth. Rev 12:3–4 NIV
And especially this one, which gives the Number of the Beast:
Then I saw a second beast, coming out of the earth. It had two horns like a lamb, but it spoke like a dragon...It also forced all people, great and small, rich and poor, free and slave, to receive a mark on their right hands or on their foreheads, so that they could not buy or sell unless they had the mark, which is the name of the beast or the number of its name.
This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man. That number is 666. Rev 13:11,16–18 NIV
It should be noted that as an angel, aside from a stint in fleshly imagery in the West, Satan like other angels is considered to not actually have a 'true appearance' at all. He is a bodiless intelligence and is thus, invisible.
It is highly misleading to try to tack down his appearance, like that of any angel or demon, because what they are is not primarily bodily and thus, passively or objectively visible, but intelligible and intelligent, and subtle. Any image they assume can be considered a 'vision of angels', since they have no actual appearance. How they appear is based on how they wish to be intelligible to us.
If you can stomach it, you may wish to consider On The Divine Hierarchy by St. Denys.
Satan can appear as an angel of light and frankly, as alluded to above, whatever suits him and God permits.
The Bible says that Lucifer( Satan's former name)was a cherub(Ezekiel 28:14). Cherubs are not cute little chubby angels but are in truth actually pretty frightening to look at. Cherubs are twenty cubits long, had four faces(of an ox, lion, eagle and man), an enormous wingspan, huge flaming swords and are covered in eyes according to Ezekiel and Isaiah's accounts. We can only assume that Satan looks like one of these.