So far I've played the Chinese, Persians, Japanese (my very first game on chieftan) and Egyptians ... dabbled with the Americans and French, but didn't particularly get anywhere with them. I've had my most success with the Chinese and Persians.
As many have said, the great thing about the Chinese and Persians is that they may be the best triple-threats in the game -- both possess what's to me the most important trait, industrious; a genuinely useful "secondary" trait, militaristic and scientific, respectively; and both have really useful UUs. (To me, a useful UU is an offensive unit with an offensive advantage that comes neither too early or too late in the game, and doesn't hurt you in the upgrade department. Chinese Riders and Persian Immortals don't hurt you *too* much in upgrading, with Riders being better since they go up to Cavalry, while you may be stuck with too many Immortals kicking around later.) Other civs with the industrious trait either have IMO poorer secondary traits (Americans and French) or poorer UUs (Americans, French and Egyptians).
I'm also playing an older version of the game where you can't upgrade into your UU, but have to build them from scratch. There seems to have been some complaints about this on this forum, before whatever mods or patch changed this, but I actually use the restriction to my advantage ... or try to!
With both the Chinese and Persians, I'm not really building all that many of their UUs' predecessors on the upgrade path (horsemen and warriors), so I don't really mind having to build a few extra from scratch to go on the offensive when they come around. Meanwhile, this means I can afford to let my horsemen and warriors stray really far from my borders, as I won't want to gather them back in for an upgrade for a looooooong time (riders not until cavalry, warriors ... NEVER).
So what I have is a terrific exploring, scouting and expeditionary force, from almost the beginning of the game. Especially with the Persians, I have absolutely no compunctions of sending every single one of my warriors to the ends of the earth as soon as spearmen are being produced in my cities, because I know I'll have the Immortals soon. So these guys cover the jungle and mountain exploring, and a couple of horsemen run around the 2-move areas.
The goody huts may not be as plentiful or as rewarding as with the expansionist civs, but you can really cover a lot of ground with this method, I've found, and get a pretty good take on the world map, early. (Obviously I don't play tiny archipelagos very often ...) One thing I've noticed -- I'm only up to Regent, however -- is that even the expansionist AIs don't seem to do all that much exploring compared to me. Their single scouts will do as much as they can (and pop a lot of goody huts, the bastards), but they don't seem to really put a priority on exploring the world as much as I do. Anybody else notice this?