In Civilization and Civilization II, Shakespeare's Theatre is a Wonder of the World. Most veteran Civ players don't put too much value on it.
The wonder provides one benefit: after it is built, no citizen in the city that builds it is ever unhappy again. The effect expires in Civilization, but in Civilization II, perhaps because the wonder is so weak, the expiration is taken away. Thus, for the price of 300 resources shield, you get a town that is totally happy forever.
This wonder isn't used very much for the simple reason that it is much cheaper and easier to construct a normal city improvement, such as a temple, cathedral or marketplace to keep people happy, rather then building a wonder of the world to do so. In addition, if a wonder is needed to keep people happy, it should be Michelangelo's Chapel, which counts as a cathedral in every city in your civilization, which effectivly ends unhappiness except in extreme cases.
The one time it is good to build this wonder is if you have already switched to a republic, and wish to carry on overseas trading. In that case, building this wonder in a coastal town means you can churn out as many naval units as you need without the city revolting.
Another interesting fact about the Theatre is that in both games, for whatever reason, it requires the civilization advance of medicine to build, leading to the joke "take two aspirin and see Hamlet in the morning".