As every audiophile will acknowlege, compact cassettes have a sharper audio fidelity than any other widespread format.
Jokes aside, I really enjoy having a library of the music I enjoy that I can tangibly hold. I have an utter disdain for streaming corporations, and digital music doesn't appeal to me (though I do have a pretty large downloaded MP3 and FLAC library on my laptop and thumb drives). CDs are my preferred format these days for convenience and price, but I still have a huge soft spot for tapes.
I generally prefer analog formats to digital formats; while I think the whole "warmth" thing is a little silly, I'm not bothered by the fuzzy sound quality (my hearing isn't really good enough to distinguish it most of the time anyway). Tapes are a lot cheaper than records, and have the added bonus of recordability. I love making mixtapes, and appreciate the ability to record an album that would otherwise be pretty expensive to acquire. Plus, I greatly enjoy the actual recording process. DIY ethos is cool and fun.
There's also the aspect of portability; taking a walkman and tossing a few tapes in my truck is a lot more convenient than having to lug my entire stereo setup and records somewhere. it's either that or MP3s on my PSP.
