1) To allow US oil companies access to Iraqi Oil. They would not steal the oil as some suggest, but negotiate terms with an Iraqi government to extract and sell the oil in exchange for payments to the Iraqi government. In exchange these companies would provide campaign support, Jobs and other benefits to Republicans in congress and the administration, and their family members, thus strengthening the political position of the party. This mission has been successful.
2) To provide lucrative business opportunities to US Contractors such as Kellog Brown And Root, Halliburton, Bechtel, and others for the rebuilding of Iraq, servicing of the troops, and some militatry functions as well. In exchange these companies would provide campaign contributions, Jobs (such as the one Vice President Cheney recieved from Halliburton, with no prior experience managing a large company) and other favors to Administration officials and members of congress, thus helping to strengthen the position of the party. This mission has been successful and in 2008 you will see large numbers of Bush administration employees and their families accepting lucrative jobs from these companies and their affiliates.
3) To protect US interests in the area such as Israel and Saudi Arabia. By moving bases from Saudi Arabia to Iraq and building up bases there, the US could (it was thought) exert more military pressure on regiemes such as Syria and Iran, who might threaten Israel or oil production in the region. This mission has failed, as Iran's influence in the region has spread into Shia-controlled territories, putting Israel and oil production in greater peril.
4) To benefit the legacy of presidents HW and GW Bush. The idea was that we would "finish the job" started by Predient HW Bush and transform Iraq into a western style democracy, thus portraying the presidents as visionary and having transformed the world for the better. This mission does not appear to be going very well, but time will tell.