I prefer the early middle ages or "dark ages" for heroic flavor, flexibility and as a long time personal historical passion. It works for fantasy or historical gaming, and it is pretty easy to blur the lines between the two.
From a role-playing perspective, the lack of social flexibility in the historical high middle ages in western Europe is a bit stifling, though it can work on the geographical fringes. Of course in fantasy, that can all change. In fact, I wonder how many people even think about their fantasy games in historical terms.
The Renaissance era seems to be the default for fantasy. I'm not sure why. Perhaps it easier for moderns to relate to an imagined society on the edge of capitalism and technological wonder. Historically, I would argue that the Renaissance didn't even exist as an era, even though it has long been a part of the western narrative. It was, I think, essentially an artistic movement that was limited to a small number of elites in Norther Italy. The vast majority of Europeans were completely oblivious that they were living in a new enlightened era of humanism. The plague, the expansion of trade, and later the Reformation, had much more to with the breakdown of feudal society than Renaissance thinking did.