About a year ago, I decided to buy the 1982 version of The Thing but didn't settle for the 1998 Collector's Edition as I didn't like the cover art, so I hunted down the region 1 2004 Collector's Edition which was tough to find considering I live in Australia. The 2004 release cost about $10 more then the 1998 release, but I was willing to hunt it down as I was a fan of the cover design. Same thing applys with The Terminator, I had to search deep for the definitive edition and when I did find it again I relised it cost more then any of the older special editions however I still ended up buying it despise the fact that both the 04' collector edition of The Thing, and the definitive edition of The Terminator were basically the same discs from there original counterparts..

Yup. Done that. But I normally buy the Special Editions anyways.
But I've had the reverse problem; the barebones had a better cover than the Special Edition (eg. Prince Caspian, Mamma Mia!) so had to buy both, swap the covers, and then re-gift the barebones DVD with the less-attractive SE cover to a relative who doesn't care about special features. I bought the Thai PAL release of Phantom of the Opera to get the cool embossed black slipcover cover with the mask and the rose to put my R1 discs into.

Yeah, I did that on the HMV exclusive Hot Fuzz R2 DVD

Not really. Can't think of a time I have.

Kinda yes I guess, I replace almost everything with downloaded covers for thinpak and usually get better looking covers that way, plus you can get some really awesome matching collections that look great on a shelf and makes DVDs a really good talking peice when company is over

The cover art doesn't have the slightest bearing on the quality of the film. So in answer to the question: No, because I buy my films to watch them, not the cover art.

I am in the same boat as JJE. If the original cover is decent, I can use a scan of the original, otherwise I go custom. I personally like the spanning spine covers for collections of films, or seasons of tv shows.
Other than that, the only cover I will pay more for is a Steelbook, just because I like that kind of case.

I've recently been hitting the used stores to pick up original releases of Conan The Barbarian, Young Frankenstien, Animal House, For Love of the Game, American Grafitti, and others that have better cover art than the version available now. Since I hate BD packaging, I'm going to use them to store the BD version when I upgrade...

Sometimes I will if I really like the art. Especially for movies I enjoy that have the original poster art and an edition comes out with some photoshopped floating head piece of crap "art."

No way in heck! All I can see of the DVD on the shelf is the spine anyway!