I know the functional effect of unchecking a song: it doesn't play (except when explicitly double-clicked) and doesn't sync with an iPod/iPad. But how is this useful? Does Apple officially recommend any sort of usage of the checkboxes? Or, more subjectively, do you make use of the checkboxes in iTunes, and if so, what songs do you check or uncheck and why?
I think you sort of answered your own question as far as "usefulness" of the feature.
As far as a use case I would use the check boxes more when I had a larger capacity iPod that could fit my entire music library. The songs I would uncheck would be skits on hip-hop/rap albums and I have a few theme songs from movies or tv shows I would also uncheck. I would then select the "Only sync checked songs" option in iTunes so I would only have to plug my iPod in and it would automatically sync my library except for those that were unchecked.
Almost all the answers so far seem to be things where a smart playlist might be a better solution… but given that, here's mine:
There are a lot of bands that have one great album and a few hit-or-miss albums. For them, I buy the good album + the greatest hits.
But that leaves me with duplicated songs. Yes, they're really good songs, true, but they're still dupes. Those, I check off so they only show up once.
They can be used to solve the dreaded "remove all files with exclamation marks" problem. See https://apple.stackexchange.com/a/35813/646
I typically don't uncheck tracks, but when I do, it's typically because I've ripped an entire CD, and there are tracks that I don't think I will want to hear, except on rare occasions. If I wasn't completely pedantic about having everything I own in my library, I'd probably just delete those tracks, but I don't want to have to dig the CD out of a box and re-rip it, should I change my mind in the future.
I think most other uses are better supported using smart playlists. IMO, checkboxes became mostly pointless after Apple introduced smart playlists.
In my case, I've added an audiobook to my iTunes to listen to on my iPhone while I'm out of the house and want to, but can't, read my book. (I get carsick while reading, etc.) However, it's 20 discs long and averages 20 tracks per disc. I want to keep it in my iTunes because I spent quite a bit of time adding all of these discs and adding information, but I also don't want to have it popping up with my music randomly! Also, I don't want to bloat my poor phone with the entire thing. So I sync like four discs at a time, and uncheck the ones I've already listened to and ones I don't want on my phone yet!