The best thing of all to rush is a temple, if you're a religious civ. Temples cost 30 shields, and any rush of <20 shields will cost you only 1 citizen.
Conveniently, a city built with a grassland in range can grow after 10 turns and produce at least 10 shields in 10 turns.
That means that if you really want cultural expansion in a city fast, you can build the city, spend 10 turns building a temple, and then rush it. The happiness effect of the temple will counter-act the unhappy citizen for the 20 turns, and after that you get the full benefits of the temple. So, all it's really costing you is one citizen.
Because of this, religious civilizations can afford to settler two spaces away from important resources, while other civs have to settle right next to them, because non-religious civs will take MUCH longer to get any kind of cultural expansion early.
A little later, libraries can be whipped out for scientific civs, but you have to have 20 shields in the box if you only want to lose one citizen, and they don't have the happiness-counteracting effect. Also, I usually try to get republic before literature anyway.
Barracks are a good thing to whip for militaristic civs, and you can also whip troops, especially if you desperately need them in an early war. Archers, spearmen, and perhaps horses and swords are the most likely whipping targets.
But, aside from the religious-temple thing, I actually don't whip all that much.
-Sirp.