Well, the key really is to not be dependent on any one thing. Don't depend on Immortal rushes, getting the Great Library, having the Militaristic civ trait, having a food bonus by your capital. Take advantage of these things, sure, but don't become dependent on anything. Then there are no limits.
I don't even remember what the civ traits are for the most part. But notes on a few of the above:
*Germany is militaristic and scientific (checked the editor) and gets Bronze Working and Warrior Code. Very good for early wars with those two traits, so long as Greece or someone like that isn't your neighbor. After that it lags for awhile, but a Scientific focus can allow you to become powerful in the late Middle Ages or especially with Panzers.
*The Zulu, with their Impi, are great at pillaging improvements. The AI can drive you nuts with this, and you can do the same to them. Too many swordsmen attacking you? Send in three or four Impi to search out the Iron and pillage it. Works much better than Chariots or Spearmen.
*Portugal, with their Carrack, is awesome on the seas at the time of Astronomy. Basically it's an early Frigate that can transport troops - so I'd almost advise holding off on Magnetism and researching Navigation for the ocean-going part, thus allowing you to build lots of what are essentially cheap frigates.
*The Celts make for a dangerous offensive civilization with the fast and powerful Gallic Warrior. They're a popular choice in Always War and early war games.
*The Samurai of Japan makes for a great defensive unit as well as offensive. They can hunker down in cities to defend, and if a lone Longbow comes along, they aren't stuck with defence like a Pikeman but can go on the offensive and slaughter it.