Courthouses just halve the maintenance you see in the top left of the city screen. Mousing over the details there should give you all the info you need comparing courthouses to gold multiplier buildings (I think... played BUG for so long that I can't recall details of the regular interface). In the late game, don't forget to adjust the maintenance for inflation (check your economic advisor).
On higher difficulties, maintenance can cost a pretty penny, and in a pure production city just working farms and mines that can well exceed half the total commerce.
There are few 'always do xyz' in civ, and it would be a worse game if there were more... but building a courthouse early is rarely a flaw unless you obviously have something more important to do.
If your approach to new cities is 'build infrastructure first, worry about money later', courthouses should be a high priority because they save money even in your building phase. If you don't take the time to build infrastructure before ('screw hammers and long-term benefits, there's always a crucial research to be done/bills to be paid NOW'), courthouses lose a lot of their appeal, but I'm not sure how competitive this approach is on the higher levels.
Celebithil made a good point about corporations - if you rely on them, courthouses are your most important buildings.