First city -- warrior, warrior, warrior, settler (unless expansionistic, then replace warrior with scout) -- barring bonus resources making things easier. Then usually granary.
Later cities -- warrior, worker/temple.
At this point, I basically never build libraries, universities, research labs, colusseums, coastal fortresses, and rarely build walls.
Depending on my civ's traits and city locations, it's usually defender, temple, settler, ... There's not really a set pattern -- see what the city's good at and take advantage of it.
Does it have lots of shields but limited food? I use those as my main military producers.
Lots of food? Granary and then settlers/workers (or other order)
Near luxuries? Temple/worker early to get as many luxuries as possible hooked up.
On the sea? Temple (if can get a bonus this way), harbor, or worker.
Semi-corrupt? Courthouse gets high priority (almost as good as a factory, in its own way). One of these usually gets an FP ordered.
Hopelessly corrupt? Workers/temple.
Need the enemy? Barracks/temple, depending on borders.
(Many temples can be replaced with library if scientific, but I am tending to steer clear of scientific civs at the higher levels).
Later builds depend on some of the same things. I try to get my "first-ring" cities (those ~6 nearest the capital) with a marketplace ASAP. Most get temples and granaries, too.
Wonders? Too many shields for too little benefit, usually. On regeant/lower, I might, depending on the map.
Arathorn