What are the economic ramifications of rent control? What effect do they have on renters?  Landlords? Are there examples of rent control working, improving living conditions for renters?  

I.e. What are the main arguments for/against rent control (purely economic, not emotional or moral).
Well, rent control is the classic example used in many economics textbooks when talking about price ceilings. A price ceiling is a maximum price one can pay for a good, and is set by a governing body. There are many cons to price ceilings and not many pros.

$\textbf{Pros:}$

1) Because tenants of the property know that apartments are in short supply, they will have an incentive to take good care of the place in order to stay on the renter's good side because they may not be able to get another apartment if they get kicked out of this one.

2) Tenants who get apartments will have lower rent costs and will therefore be able to spend/save more of their money. If they choose to spend it, that can boost the local economy because more money will be spent in local businesses.

$\textbf{Cons:}$ 

 

The graph above depicts a binding rent control. By this, I mean that the rent controlled price is below the equilibrium price. In this example, the rent controlled price is $1,000$ and the equilibrium price is $1,500$. What this causes is a shortage of apartments. Looking at this graph, we can see that at the price of $1,000$, $Q_D=2,100,000$ and $Q_S=1,900,000$. Using this, we can see that the shortage will be: 
$$Q_D-Q_S=2,100,000-1,900,000=200,000\;apartments$$

What this means in words is that there are more people who want apartments than there are people who are willing to supply apartments. What might be the side effects of this?

1) Rationing: There are a couple of ways rationing may occur, but in the market for apartments the only way which makes sense is rationing through discrimination by sellers biases. What this means is that the renter may give the apartment to someone who doesn't value it as much as another person based on their biases.

2) Illegal activities: One thing which may occur due to rent control is under-the-table deals. Basically, people may pay the seller some money under the table to ensure that they get an apartment.

3) Homelessness or relocation: We need to look at what we mean by the quantity of apartments demanded is greater than the quantity of apartments supplied. What this means is that people who want/need to buy apartments will not be able to (in our example 200,000 people at least). What are the two outcomes of this? The first outcome would be homelessness because people cannot get apartments, and they may have nowhere else to go. The reason why this is not desirable is pretty obvious (we don't want people to have to live on the streets). The second outcome would be relocation of current residents. What this means is that people will need to move out of the area. This will hurt the local economy because less people will be spending their money in local businesses.  

One last thing to keep in mind is that over time this shortage will get worse. In the short run, the sellers may not be able to take the apartment off the market. However, in the long run, sellers may decide to sell the apartment complex, which will cause the supply of apartments to decrease even more. This will exacerbate the problems I listed above.

$\textbf{Edit:}$ Another problem caused by rent controls was mentioned (quite astutely) by $\textbf{AdamBailey}$. He pointed out that landlords may not make enough money to maintain his or her rental properties, and over time the quality of such rental properties may depreciate drastically. This shows that, not only will the quantity of apartments decrease, but the quality may decrease as well. This is another perfect example of how rent controls can hurt those that it is trying to help.