There's a certain amount of ambiguity to the question, but that's to be expected. I'll provide a few examples.

For democracies, one of the more notable cases is that of the Icelandic parliament, or Althing. The Althing was founded around 930 C.E., and is considered one of the oldest democratic governing bodies in the world. In its origin, the Althing allowed local chieftains to meet and discuss issues of other topics of conversation. However, Iceland was governed by both Norway and later Denmark, and the Althing had a brief period of interruption. It has, in the most part, continued in a similar form for most of its history, and the Icelandic legislative body is still referred to as the Althing.

From here and here- a PDF on the official website of the Althing.

Something else you may want to consider is imperial China. While not still in continuation today, China- as an empire of one kind or another- existed throughout much of history. Rulers, lands, and customs changed, but the overall idea endured for quite some time.