A form of government where the most wealthy people (or person) rules.
A form of government wherein people lead based on how good they are, for example, a great general could lead the military, while an economic expert could control the finances of the nation. Most of the times, these people have to keep proving their worth however, so if one makes but a single mistake, he is replaced. This is also known as a tekhnekratia.
A form of government where the best person leads for a set duration. Most of the time's, who is the best is decided by competitions, like a sports competiton, or an IQ test.
A form of government where the people (everyone who is a citizen and wants to) vote on matters and propose matters. A small group of people who can't vote on matters nor propose them count the votes and such. Leaders are appointed when needed, like generals, but only for as long as the people want it (if one doesn't, and proposes to remove him (or her), and the majority agrees, then another one needs to be appointed). A demokratia is also known as an isokratia.
A form of government where an elected leader leads for a set duration, which could be his entire life.
A form of government where a leader and his heirs, and their heirs, et cetera, rule. Sometimes all heirs rule, but since that eventually results in a thousand leaders, most of the times an heir is appointed by the leader to become the new leader when the leader dies (or sometimes before the leader dies). It doesn't matter how the original leader got in power. It is also known as a monosarchoon (which is nearly never used), but most of the time I'll simply use monarchy (monarchy comes from the Greek words 'monos' (single) and 'archoon' (ruler)).
A form of government where the most powerful one leads, most of the times by killing or subdueing his enemies, not to be confused with an aristokratia, where leaders are chosen by legal and non lethal competitions. Often, this results in a phobokratia (also known as a deimokratia) where the leader (and perhaps a government created by the leader) inspires fear and terror into his subjects (like the Soviet Union of our timeline).
A form of government where there is no government. Quite a paradox.
A form of government where the military and the state are one and the same. The military leads the nation, which most of the times is focused around the military (for example, most of the times each citizen automatically serves in the military).
A form of government where a leader rules by the right of god, and basically is god (or the personification of god). The nation is governed following god's laws. It doesn't matter how this leader got in power.
A form of government where the people (everyone who is considered a citizen and wants to) vote on a person out of a group of people (who can't vote). A smaller group (they who have gotten the most votes) will rule the nation, as long as the people want it (they can sometimes propose a reelection, but there's always a set period of time before reelections anyway). The 'X' in xeirotokratia is pronounced like the ancient Greek 'chi'.
More will possible (probably) be added.