I can't believe people don't get this, but here's the reasons we invaded Iraq.
Persian Gulf Wars
Iraq invade Kuwait to add more land onto the Iraqi Empire. The USA was trying to liberate (not invade, liberate) Kuwait and then defeat the Iraqi invaders.
War on Terror
9/11.
Really? Here was me thinking that Iraq invaded Kuwait because the Kuwaitis increased oil production and kept oil prices down, seriously damaging the economies of Iraq and other OPEC members, while also demanding massive payments from Iraq to cover national debts incurred during the Iran Iraq war*.
There was no "Iraqi empire". Iraq did not invade Kuwait to conquer territory, but to free themselves from a form of economic subjugation by the Kuwaitis (a tactic of international relations that the Kuwaitis no doubt learned from the ruthless and greedy US).
The US stepped in for many reasons, but again largely economic ones. The US economy depends on cheap, underpriced oil from the middle east, and Kuwait would almost certainly not have defied OPEC and increased oil production without gaurantees of US protection.
*Edit: remember the Iran Iraq war? That was when the US and Kuwait loaned money to Sadam Hussein, and the US sold him plenty of weapons, including chemical weapons, for his war on Iran.