The supply and demand model is the workhorse of applied economics and is a topic that most students learn in a first-year course.
In our class, we discussed a couple of applications that showcase the use of the supply and demand model.
First up is the topic of rent control. There are many readable introductions (one from the Cato Institute is here) to the topic and the basic conclusion is simple: when price is held below the equilibrium price, we expect two offsetting effects. First, since the price is lowered, we expect the quantity demanded to increase. In other words, the number of rent-controlled units that will be demanded will increase. Note that this has nothing necessarily to do with housing "need": At a low enough price, people will move from homes to rent controlled dwellings, regardless if they "need" a place to live. On the other hand, the lower price induces producers (i.e. landlords) to under supply the market. The result: a deterioration of the housing stock.
Another topic of discussion is the application of supply and demand analysis to the redemption of slaves in Sudan. A nice book length treatment is provided here--Buying Freedom: The Ethics and Economics of Slave Redemption. The basic idea is that if redeemers are willing to pay a high enough price for a slave (to ultimately be released) is there now an incentive to capture more individuals and offer them up for redemption?
The study of supply and demand can be utilized to study a variety of topics with some surprising results.