Slavery. Slavery fixes unhappiness. I struggled on Prince until I realized the power of Slavery. Afterward, I started slumming on Monarch, winning the vast majority of my games.
Let's say that you've got a city the size of 15, 4 of which are angry and refusing to work. Sure, you could fix this in a number of ways that don't involve whipping your populace, such as building a theater, increasing the culture slider, and/or switching to Hereditary Rule. But why not get some production out of those unhappy people, especially after you've already explored some of the other options? My rule of thumb: if they're still too lazy to work after building a market, theater and going to 10% culture, then they deserve what they get.
Let's say that you're building a University. It's going to take 50+ turns to complete in this city, because most of the tiles offer no production (for example, coastal tiles or cottages). You want to hurry this University, because Oxford is a critical National Wonder. Oxford University grants +100% research to the city that builds it, but it requires a certain minimum number of Universities before it can be built. Universal Suffrage is an excellent alternative to Slavery (if you have enough money per turn to waste hurrying stuff, that is), but it comes much later in the game -- with Democracy, a technology that requires several more discoveries after Education.
How can we solve these two dilemmas (angry people + wanting to hurry our current building) at once? Slavery. Slavery converts your excess population into production. There are two important rules: 1) Each citizen is worth 30 hammers and 2) You can only slave away half of your population at a given point in time. Since you have 15 people in this city, your limit is 7 people lost to slavery. 7 * 30 = 210 hammers (I'm too lazy to open the game just to check, but I think Universities are around 200 hammers). As long as your current job costs 210 hammers or less, you're all set! Just switch to Slavery (if necessary), click on the "hurry" icon, and watch all that unhappiness fade away! Of course, this city will be left with a -1 unhappiness penalty from using the whip on it, but since you lost all those citizens to Slavery, it's going to take a while before you notice the unhappiness penalty.
Uh, I probably didn't do a very good job of explaining Slavery. Check the War Academy for much better (and probably more concise) explanations.