What's the point of the second commandment? If the first commandment, "Thou shalt have no other gods before me" means that God, and God alone is to be worshipped, why do we have the Second Commandment? 

Aren't idols covered in the First Commandment? Worshiping an idol would be "having another god" before the Lord, and we don't have extra commandments covering lust (just the one general one on adultery) so why the extra commandment?

Note: I've answered this myself from a Protestant/Reformed view, but I'd love to hear what other traditions have to say and my answer is by no means an exhaustive one
The First Commandment covers who to worship, but the Second Commandment covers how.

Often when the Israelites worshiped idols they were actually trying to worship Yahweh[citation needed] and were going about it all wrong. In the Second Commandment, God was giving a clear explanation on what kind of worship was acceptable, and idolatrous worship was out.

From a reformed protestant point of view, I understand this to be forbidding prayer to or worship of images of God or Jesus. 

Neil Postman, author of Amusing Ourselves to Death (and also Jewish, I believe) comments:


  I wondered...why the God of these people would have included
  instructions on how they were to symbolize, or not symbolize, their
  experience. It is a strange injunction to include as part of an
  ethical system unless its author assumed a connection between forms
  of human communication and the quality of a culture. We may hazard a
  guess that a people who are being asked to embrace an abstract,
  universal deity would be rendered unfit to do so by the habit of
  drawing pictures or making statues or depicting their ideas in any
  concrete, iconographic forms. The God of the Jews was to exist in the
  Word and through the Word, an unprecedented conception required the
  highest order of abstract thinking.


While Postman is using this as example of how different media affect their cultures, it's interesting to think about it in light of the New Testament and Paul's statements about faith and sight. 


  For we walk by faith, not by sight. - 2. Cor. 5:7


and also


  For in this hope we were saved. But hope that is seen is no hope at
  all. Who hopes for what they already have? - Romans 8:24


The idea seems to be that we are to walk by faith, trusting in the Word of God and not in the tangible images we might construct. We are to worship God by faith, not by sight.