The Yamato dynasty, the ruling house of Japan, claims to have been on the throne since about 600 BCE, which would make that a 2600 year run. There is solid historical evidence for the family line since the 6th century that is generally accepted by scholars, so that's 1500 years of a single ruling family (although the emperor was not always in real control, those in control always claimed to rule in his favor, whether they really did or not is another story entirely).

That's the longest I can come up with, unless you count Pharonic Egypt, as /u/reslumina/ mentioned, but they have several "intermediate periods", dozens of dynasties, and even an "old" and "new" kingdom, so I'm not sure you can really claim that as the "same" government the whole way through.

National governments, or smaller governments as well? The oldest continuously inhabited cities are in the fertile crescent like Aleppo, presumably those cities have had some form of self governance for many thousands of years.

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