While speaker drivers and crossovers are very important, they're generally quite useless without a box to put them in. In fact, a woofer's frequency response is determined largely by the box it is used in - without a box, they won't work very well at all.
There are basically five kinds of boxes: Sealed boxes, ported boxes, horns, transmission lines, and open-baffles. Each performs very differently, and each has its own benefits and hindrances.
Sealed boxes, like the name suggests, are air-tight boxes into which drivers are placed. Because there is no way for back-pressure created by the driver to escape, these are sometimes also called "acoustic suspension" speakers. They have a -12db/octave roll-off below the tuned frequency, although this will vary between box and driver. In addition, the lack of other resonant objects aside from the air in the box eliminates potential sources of distortion.
Ported boxes are similar to sealed boxes, except that they have a hole or tube - a "port" - that resonates at a pre-determined frequency. Because this "port" allows a point of resonance of a lower frequency than the box itself, it can help increase response at low frequencies. However, the roll-off is a steep 24 decibels per octave - eliminating some very low frequencies entirely. Furthermore, the port can cause unwanted resonances in the driver, and may cause distortion if not designed properly.
A horn works a lot like the instrument which shares its name: Small at the end with the speaker driver, and large at the other. However, many horns incorporate resonating chambers and reflective sections to compensate for frequency response, making them far more complex than a simple expanding pipe.There are generally two variants of horn: Front-loaded horns, which go on the front of the driver and face towards you, and back-loaded horns, which go behind the driver. While front-loaded horns - which more directly affect the sound which travels to your ears - can cause distortion if built improperly, they are also generally very, very efficient - they work like an old-fashioned megaphone, which despite having no electronic parts can make your voice effectively louder.
A transmission line works like a horn, except backwards. The general concept behind a transmission line is that they are in essence a tube behind the driver, stuffed with a filling- usually some sort of fiber-based fluff. The longer the wavelength, the more fluff a single quarter-wave of the frequency will have to travel through,. The physics and design of transmission lines is very complex, and requires some sophisticated mathematics for modelling them - however, the bass performance of these can be impressive indeed.
Open baffles really are not boxes at all. Instead, they're just a flat plate - a "baffle" - that allows for reflection of sound waves off of it, and prevents vibrations emanated from the front from being eliminated by vibrations from the back. Open-baffle speakers are generally poor in terms of bass performance, as low frequencies have a wavelength long enough that it would require a massive baffle to prevent bass from self-neutralizing. However, so long as they are placed a suitable distance from walls, the lack of back-resonance can eliminate a large amount of distortion. For this reason, open-baffle speakers are very popular, and a mid-woofer in an open baffle is often combined with a woofer in a ported box.
Tomorrow: Baffle step, and what exactly is, anyway.