Theres a few facets to this answer.
A. the audiophile: listens to records because thats the oldest form of recorded music, and does it due to habit, nostalgia, and because they feel its the truest and their most favored way to listen to music.
B. The collector: often a facet of the audiophile...collects vinyl, often times because of rarity, collectibility and/or because it often features more or better art, better for signatures or displaying, and overall, has the most redeeming quality for pride of ownership factor.
C. The old schooler: Someone who started buying (or collecting) music long before cds or cassettes were out, or maybe just appreciates the sound or quality of vinyl records over the modern technology alternative. They often are biased or just further enjoy the aesthetic of vinyl records enough to never or not very often care to try or purchase other forms of music media.
D. Availability and Practicality Junky: Someone who prefers the cheap prices of older vinyls (often a few dollars) instead of $12-17 sticker prices of CDs for the same album. They like owning the music, as opposed to downloading, but dont have a lot of cash to spend OR just want more bang for their buck. Also, many albums are hard to find on CD or maybe just arent pressed to CD yet, so locating older vinyl copies of these albums is sometimes necessary.
Now, for me personally...the main appeal of vinyl was because with older (classic rock, progressive, psychadelic, jazz and other various vintage recordings) albums, the vinyls indeed DO sound BETTER. THis is often because the CDs made of old albums are recorded from the original vinyl pressings, and thus have the "i sound like a copy" atmosphere to them. This is often not noticable to most people, but i was able to tell after a bit of time. Also, i enjoyed collecting, and the feel, the hunt, even the smell of classic albums in their original format...its almost more personal of a relationship. However, they do wear out, and get scratched if youre not careful...and eventually take up a lot of space and inevitably, made my home smell like a garage sale once i got enough. I have now sold off most my vinyl, and replaced them with the CD versions. They sound almost as good, but i do admit...a feel...an atmosphere and a vibe is missing from those albums. I also dont have to pay $200-500 for rarity vinyls and obscurities anymore...i can now find the reprints on CD for $12-25 depending on import prices, which obviously is much more financially attractive. I do however think its very silly to buy vinyl albums of current and new releases. They dont sound any better, theyre heavier, get worn out easier, and you cant take them in the car or anything else of that nature...not the most efficient form of listening. Thats why i dont understand people who own 20 versions of Opeth, or Katatonia, or Emperor or Nile records on vinyl...the CD would be the exact same thing for listening purposes. But if you collect, thats another story i suppose.
to each their own...