For better or for worse, headlights don't typically fail outright; they get gradually dimmer over time before failing completely. However, dim lights might or might not be the result of a failing bulb, particularly if you use certain types of projector headlights that won't dim before going out.
This is probably the case if one headlight is slightly dimmer than the other or if you've got old sealed-beam lights. Newer halogens, projector beams and xenon bulbs will generally dim slightly before blowing out, but most likely not enough to be noticeable to the average driver. Sealed-beam headlights will dim themselves practically out of existence, eventually going from a weak white to a sickly yellow before failing.
Headlights are one of the most amperage-hungry appliances on your car, which makes them far more sensitive to drops in current than most other systems. Loose, corroded and frayed ground wires will reduce current flow through your system as a whole, and will result in noticeable dimming in the headlights. Watch your instrument cluster; if it gets dimmer when you engage the bright headlights, then take a look at your battery terminal connections and the negative ground strap on your battery or engine, and clean them if necessary.
A worn alternator will manifest most of the same symptoms as a bad ground, but headlight brightness will generally rise or fall in direct proportion to engine rpm. Of course, that depends on the exact fault in the alternator itself; a bad voltage regulator that provides consistently low voltage may continue to do so regardless of engine speed. Older vehicles often use an external voltage regulator, but newer units are built right into the alternator. The surest test is to use a digital multimeter or voltage meter to check power supply right at the lights' wiring harnesses.
Acrylic headlight covers may look snazzy from the factory, but they're much softer and more vulnerable to damage than the old glass lenses. As you drive down the road, dirt and dust particles constantly sandblast your headlight covers to a milky haze. This, combined with surface yellowing of the plastic will dim your headlights by diffusing the light instead of allowing it to project cleanly through, although this problem will generally apply to both headlights equally. Fortunately, the fix for this problem is pretty easy; a bit of plastic polish and a rag may help to shed some light on your diffusing dilemma.
