I stumbled across this fairly interesting (if also fairly obvious) Washington Post op-ed piece by Anne-Marie Slaughter:
In summary, she argues that far from being irrelevant, the UN Security Council has lately been doing exactly what it was designed to do. (And in passing, she clears up a mystery I'd wondered about for a while: How could US forces in the Korean War have operated under UN auspices when North Korea's patron the Soviet Union had a veto in the Security Council? Answer: The USSR was boycotting the Security Council when the resolution authorizing force was introduced.)
Personally, I think the surest route to irrelevance for the Security Council (albeit not the UN as a whole) is if it appeases one particular irrational unelected leader I can think of with expansionist delusions, and turns itself into nothing more than another arm of US foreign policy. The world already has the US State Department, the US Department of Defense, and the CIA; it doesn't particularly need another body serving exactly the same interests.