When can the governed form a new government?

Answer 1

Answer, sort of.Short answer: Whenever.
Longer answer: There are several ways a government can be overthrown, some legal within the particular governments framework, some not. First let us look at the republican democracy in the United States.
The US Constitution provides a few clues. First, the enitire House of Representatives comes up for election every two years, it is possible though unlikely that all of the incumbent members fail to get reelected and a new House is formed. What happens more often is some members do not seek reelection, some fail and some succeed, and the composition of the House changes. In the Senate, one third of the members are elected every two years (remember Senators serve a six year term). This causes a more gradual shift in the composition. Dramatic examples of what can happen can be seen the the 2006 elections where the Democrats took control of both houses and thus all committee seats (research how the legislative branches of the US gov't work to see how important that is) and in the 1994(?) campaign where the opposite occured. The US executive (President and Vice President) are elected every four years and this change can arguably have more impact than the legislative elections. The constitution also provides for impeachment proceedings, which allows the populace to remove the executive, albeit by proxy through the House and Senate.
Many of the democratic nations use the Westminster system of government, wherin the sovereign (if one exists) or other head of state calls for a parliament to convene. The members of parliament are elected by the populace, the party in the majority then get to form the government. If no majority exists a coalition must be formed. This system can see a much higher rate of change as elections are not on a fixed schedule.
Then we have the non-democratic nations. Dictatorships, monarchies, and single-party rule. Peaceful change in these nations is much less likely as the rulers often do not rule with the consent of the governed. This I think is the heart of your question. When does it become appropriate for a populace to forcibly change their government? There is no clear cut answer for this, no real benchmark where a person can say "Yep, those are freedomn fighters, not terrorists (or whatever)." This is a question that requires much reading and discussion to form something like an answer. Start out with the Federalist Papers. Ask yourself why did some in the colonial US feel it was appropriate to use arms and violence to establish their own gevernment. Why did others feel that was wrong? Also, read up on the Jeffersonian idea of how the US should be governed, compare that with what Hamilton had to say. and compare both to how it actually turned out. Branch out from there.

Answer 2

According to the Declaration of Independence, the governed can form new government whenever their current form becomes destructive of their rights and liberties. However, "Prudence indeed will dictate that governments long established should not be changed for light and transient causes."