Now a senior US official has added Libya, Cuba and Syria to the list.
President Bush's pointed reference to Iraq in his State of the Union address suggests that he intends to take some kind of action against Baghdad before the end of his presidency.
Military budget: $1.4bn
Army: 383,000
Combat aircraft: 200-300
Missiles: Small number of short range surface-to-surface types
Weapons of mass destruction: Reportedly trying to produce nuclear, biological and chemical weapons
Despite years of weapons inspections by the United Nations and international sanctions, Iraq is suspected of still wishing to pursue programmes to develop nuclear, chemical, and biological weapons, and missile developments.
Analysts suggest the US would need to deploy at least 250,000 troops to seriously threaten Iraq's 383,000-strong army.
Iraqi forces are likely to be more resilient than in the Gulf War if the US objective is the removal of President Saddam Hussein.
Iraqi soldiers are already reported to be digging trenches in preparation, and the country's air defence systems have also been upgraded.
Although moderate elements have emerged in Iran and there are some signs that Washington seeks a reappraisal of relations, deep hostility and suspicion between the two countries remains.
Military budget: $7.5bn
Army: 513,000
Combat aircraft: 476
Missiles: About 200 conventional medium range Scud missiles
Weapons of mass destruction: Reportedly chemical and biological; believed to be developing nuclear weapons
Iran remains on the US State Department list as a state sponsor of terrorism. And Washington is also concerned that Iran has regional ambitions.
The US believes Iran is developing long-range ballistic missiles and weapons of mass destruction and will probably have them by 2015.
President Mohammad Khatami's support among moderates is strong, but hard-liners control the military, intelligence, judiciary and security forces.
Iran also has a strong enough navy to "stem the flow of oil from the Gulf for brief periods," according to US Defence Intelligence Agency Chief Vice Admiral Thomas Wilson.
But, according to a report from the US-based Centre for Strategic and International Studies, while Iran's conventional forces are large, much of its equipment is dilapidated and obsolescent.
Washington perceives that the most serious threat from North Korea comes from its long-range ballistic missile programme.
Pyongyang is reportedly an exporter of sensitive ballistic missile technology to states like Iran, Libya, Syria and Egypt.
Military budget: $1.3bn
Army: 1,000,000
Combat aircraft: 800+
Missiles: 500 conventional medium range, longer range in development
Weapons of mass destruction: Reportedly chemical, some biological capacity, developing nuclear weapons
North Korea is said to have ballistic missiles capable of reaching the United States by 2015,
and may have the plutonium to build one or two nuclear weapons.
Pyongyang, however, is complying with an agreement to freeze aspects of its nuclear programme, and the country remains beset by a famine.
In its final years, the Clinton administration appeared to make progress in attempts to engage North Korea in dialogue.
However, 37,000 US troops remain deployed in South Korea to counter the threat from the North's one million strong army, and President Bush seems to have put any hopes of further rapprochement firmly on ice.
Syria has never shown serious interest in producing nuclear weapons, but the country is said to have a well-developed chemical weapons programme.
Military budget: $0.8bn
Army: 235,000
Combat aircraft: 589
Missiles: 200 Scud B, 80 Scud C medium range
Weapons of mass destruction: Reportedly chemical weapons, biological weapons research
This is reported to have started in earnest after clashes with Israel in 1982. By 1984 Syria had set up two chemical weapons plants producing significant amounts of nerve gases such as Sarin and VX.
Syria currently has a range of medium range surface-to-surface missiles, including Scud B mobile launchers, Russian-built SS-21's and longer range Scud C missiles.
While the army is large, with about 235,000 active troops, much of its equipment is relatively obsolete.
The Syrian air force is also considered largely out-dated, with a token strength of exported MiG-29 and SU-24 strike attack aircraft.
Recently, there have been fears that Syria has started to develop biological weapons - but details of the level of advancement and delivery systems of such programmes are not known.
Cuba does not possess nuclear or chemical weapons, and shows no sign of attempting to acquire them.
Military budget: $0.7bn
Army: 60,000
Combat aircraft: 130
Missiles: None
Weapons of mass destruction: No nuclear or chemical weapons, very limited bio warfare research
The country is believed to have a limited biological warfare research programme - but the scope and extent of this are not known.
In 1990, Cuba possessed perhaps the most advanced air force in Latin America, with about 150 Soviet-built MiG 23 and 29 fighter aircraft.
However, the collapse of the Soviet Union - and loss of Soviet subsidies - decimated each branch of Cuba's armed forces.
The army currently has about 60,000 active troops - compared to more than 200,000 in 1994.
In the 1970s, Libya's apparent determination to acquire nuclear weapons alarmed the West. This was compounded by the Libyan leader Colonel Gadaffi's often fractious relations with successive US administrations.
Military budget: $1.2bn
Army: 35,000
Combat aircraft: 420
Missiles: Some Scud B medium range missiles
Weapons of mass destruction: Reportedly chemical, researching biological, nuclear programme stalled
While its nuclear plans appear to have now stalled, analysts say Libya has continued to develop chemical weapons. A parallel biological warfare project is thought to be in its early research stages.
Both programmes have been hindered, however, by a lack of scientific expertise.
The Libyan Government denies it is developing weapons of mass destruction.
Libya's air force has a number of medium-range Scud missiles and TU-22 bombers.
Its army is relatively small, with about 35,000 active front-line troops.