Maple, Birch, and Lauan.

Most drum shells are made of one of these woods, so we will compare them. Lauan is the softest of these woods and it is also the least attractive, which contributes to it being the least expensive of the three. For this reason it is often used in low end, budget drums. Because it is relatively unattractive, most lauan drums will be covered in a plastic. This also makes them less expensive to make, because a plastic wrap far less labor intensive than a spray finish.

Maple and Birch are what is used to make most high end drums. The choice between these drums is really a matter of personal opinion. They both sound wonderful and look very attractive with a natural finish. One little secret though: one of the reasons why maple is so popular with American drum makers is because it is the choice of Robert Keller. I won't mention any names, but many, many American drum makers buy their shells from the Keller company. There is nothing wrong with this. Keller makes beautiful shells and they've been doing it for more than 50 years, so I think they've got it down.

But Maple, Birch and Lauan each have different tonal characteristics, so lets take a look at those.
The diagrams below were provided by Gene Okamoto and the folks at Pearl Drums. Keep in mind that what most companies are using for their Mahogany shells, that we refer to as Lauan, is not the same African Mahogany that Pearl is referring to in these diagrams, but a much cheaper, less attractive, and less tonally pleasing species.

Slightly boosted lows with smooth mid and high frequencies for all around applications.

Boosted high frequencies, slightly reduced mids, and a good low end punch for applications requiring extra presence and cut.

Extremely rich low end frequencies, with beautifully smooth mids and a slight roll-off in the higher frequencies for applications requiring ultimate "bottom" and punch.  

Many people describe Maple as being "warm" and even in its frequency response. Birch is often described as "bright," because it produces more high end than Maple. The bottom line is, like most musicians, we can get pretty intense about our equipment. Because of this, we hear minute little differences that most normal people would never distinguish. Any of these woods, with the exception the lauan that budget drums are made of, will produce an equally wonderful tone. If you have certain preferences about the frequency response for your drums, choose accordingly.