This is one of those questions that pops up from time to time. It is nearly impossible to answer without very narrowly defining what constitutes "continuous government" and which parameters disqualify a nation. The most common answers are Britain or San Marino but again, it comes down to how you choose to define the parameters.
For example, using only the two listed here (revolution or overthrowing of power) I would say that the answer is Iceland where the parliment has existed without revolution or overthrowing of power since 900 AD. The problem is of course that Iceland has not been completely sovereign for more than 96 years but the parliment and therefore one might argue, government, existed long before that.
Sorry, we don't allow throughout history questions. These tend to produce threads which are collections of trivia, not the in-depth discussions about a particular topic we're looking for. If you have a specific question about a historical event or period or person, please feel free to re-compose your question and submit it again.