I do it to just mess around occasionally, but like as you know mp3 is a compression format to the uncompressed wav or .aiff or whatever you're using. Most people know this, but not everyone knows you can fool around with /how much/ it's being compressed. Any high quality mp3 you're going to get is going to be 320 kbps, to most people this will sound pretty much exactly like the .wav unless it's a particularly all over the place song, they're a big enough audiophile or they have very high quality playback equipment (a friend who shelled out thousands of dollar for high quality earbuds and the like would only listen in .flac format and had a special music player that could both hold a collection of them and is compatible with the format). Between 320 kbps and the few options lower it's not going to sound much different

https://dl.dropboxusercontent.com/u/31297091/320%20kbps.mp3

For any normal listening purposes you should stick with 320 kbps, though I know some people aren't too picky and aren't bothered by the 2 lower formats you occasionally see (256 kbps and 128 kbps). Occasionally online music stores will sell at those rates for a slightly cheaper price but I'd just suggest getting the full 320 anyways if it gives you the option.

But anyways even between those three qualities, the song still sounds pretty normal - using a converter though that lets you explore other bit rates though you can get far lower qualities which will cause some rather interesting effects to the sound as it compresses it more and more

Just compare the difference in sounds between the 4 lowest settings - at 32 kbps the highs are a lot more pshh-y if you get what I mean and the more intense moments are a bit crushed but then you get down to 16 kbps and the whole thing sounds like it's ran through earbuds playing at max volume when you're not actually wearing them. And then there's 8 kbps where the whole thing sounds like it's playing through a tube and many high frequencies aren't even included at all

https://dl.dropboxusercontent.com/u/31297091/32%20kbps.mp3
https://dl.dropboxusercontent.com/u/31297091/24%20kbps.mp3
https://dl.dropboxusercontent.com/u/31297091/16%20kbps.mp3
https://dl.dropboxusercontent.com/u/31297091/8%20kbps.mp3

Also kinda silly but noticing the drastic change in file size is interesting too (but expected really, it IS file compression). At 8 kbps the file size is 137 kb, I've wrote midi files larger than that haha

I've thought about messing around with using this sort of effect in songs before, I'll have to keep it in mind sometime in the future but it does add a new lofi feel to anything you run it through so it could compliment songs of that nature. Not to say it's a good idea to have your entire song in 8 kbps, but it could add an interesting effect to say different layers and stuff or even entire sections of songs. It's just something neat worth screwing around with, if anything it's kinda entertaining to hear what some of your favorite songs sound like taken to ridiculous levels of space-saving.

If you need a good audio file converter I'd recommend switch audio converter too btw, I've been using it for years and it's the most flexible and useful free one I've found.
http://www.nch.com.au/switch/

Getting it to run in the free version's kinda a pain to find at first since it auto goes into demo mode - it's somewhere in the options menu that lets you set it to the free licence.