Desert Storm
The United States and Iraq are currently on good terms, but they are not members of any sort of alliance.
The Gulf War was fought against Iraq to liberate Kuwait from Iraq's occupation.
Saudi Arabia's allies are mainly Islamic and Arab nations, such as Iraq, Iran, Qatar, Bahrain, and Yemen.
Iran was led by Supreme Leader Ayatollah Ruhollah Khomeini and Iraq was led by President Saddam Hussein.
Currently, as of 2015, the UK and the Republic of Iraq are allies, both committed to eliminating the Islamic State. Previously, the UK and Iraq were enemies in the Persian Gulf War of 1990-91 and the early stages of the Iraq War of 2003-2011 (before supporting the nascent rebuilt government).
United Kingdom, Australia, Italy, Spain, Poland, Latvia, Tonga.
To remove "Weapons of Mass Destruction" from Saddam's control. It's worth noting that the phrasing in the question of "its allies" is incorrect. Iraq was not invaded in 2003 by any country that it would have considered its allies. The United States was seen as an enemy imperialist power in Iraqi political circles as was the United Kingdom.
There have been numerous enemies faced by the US coalition and their allies in Iraq. They have generally been called "the Insurgency", but are composed of separate militias and paramilitaries.
Jordan's allies are: Egypt, Iraq, Kuwait, Saudi Arabia, Bahrain, Oman, Qatar, and the United Arab Emirates. Jordan's enemies are: Iran, Hezbollah and Hamas.
At the moment (July, 2014) Iraq cannot really be considered as a nation with alliances and enemies. Iraq was created out of the dregs of the Ottoman Empire and in the aftermath of two world wars. It has been a remarkably unsuccessful attempt to form one nation out of three inimical tribes. To the extent that we can consider the Baghdad government to be representative of Iraq as a whole (and it is not), the Iraq's allies are Pakistan, Saudi Arabia and possibly Turkey. Its adversaries are Syria and Iran. Given that half of the territory of Iraq is occupied and nominally governed by the terrorist group "Islamic State of Iraq and Syria" and by the Kurds of the north who would prefer an independent Kurdistan, it's even money as to whether Iraq will even exist by next year.
United Kingdom Israel Japan Canada Iraq Poland Australia New Zealand NATO and SEATO