The Bitcrusher is a very misunderstood effect, and for good reason, it completely deteriorates sound in a way that digital music has been trying to avoid for years. Any DJ website will tell you to use 320kbps MP3 files as a bare minimum. When you are mixing a track, it is recommended to use a high sample-rate, and audiophiles are in constant anguish at the sight (or sound) of a bad quality digital file. So why do people feel like it is appropriate to deliberately do this to sounds?
The easiest way to see where the benefit of a bitcrusher lies, is to compare a sample with and without it in a spectrum analyser. When you play about with the sample-rate and crush settings, you will notice that the high end is more pronounced, and new harmonics are added.
This leads me on to the first application of a bitcrusher effect. Sometimes you can actually brighten up a sound by very cautiously applying some gentle bitcrushing. In the same way you wouldn't default to cranking a distortion or saturation effect, try adding a shimmer to your audio with small touches of bitcrushed signal mixed in with the dry signal.
When you have short sounds like the hits of a snare or hi-hat, their length is often too short to be able to properly identify an effect on them. Try using a bitcrusher to create a different character to these short transient sounds, this can then be automated or attached to an LFO/Envelope to create little variations and nuances which are often lacking in electronic drum sounds. This is particularly useful because of the way drums are often looped or synthesised with the exact same unchanging sound throughout a track.
Another great application of a bitcrusher is to use it on a sythesiser, the famous dubstep "yoh" sound can be generated with a resonant filter going into a bitcrusher, seen below.
If you are layering certain sounds, adding a bitcrusher to them can allow better separation, particular in the higher frequencies, and accentuate some of the harmonics. This works very well for heavier formant basses where the high frequency content is just as important as the sub frequencies.
In a similar vein, a bitcrusher can be used on a sine sub to brighten it up, either to pop out on cheaper speakers, or to make it clearer in certain sections of the song.
For distinctly Lo-Fi sounds, a bitcrusher is the easiest way to generate a retro sound from a clean sound. Genres based on these Lo-Fi sounds don't necessarily need retro instruments to be made, instead, you could even make fairly authentic retro music from live instruments recorded through a bitcrusher. Of course, nothing will replace the old fashioned instruments with a small bitrate, but the effects can be valuable, especially if you intend to mimic the general vibes, instead of staying true to the original creation processes.
Finally, the way bitcrushers work is by shrinking the dynamic range in a very obvious manner. If you are looking for a dirty method of shrinking the dynamic range, and don't need to worry about the transparency of traditional signal compression, this method can be a really cool way of doing it. While often unpredictable compared to a standard compressor plugin, and generating somewhat messy results, it can be tastefully applied nevertheless. Just please don't replace a compressor with a bitcrusher for all compression needs!
Two great, free bitcrushing plugins are listed below: