Ok, so I’ve moved alot, had roomates, had CDs stolen, lost CDs, had CDs become unplayable. I just went to the used CD store, and found a copy of Sheryl Crow’s Tuesday Night Music Club for cheap. How delightful! I’m once again as in days of yore reveling in the sounds of “No One Said It Would Be Easy” and “What I Can Do For You” 
Other CDs I have made multiple purchases of include Pink Floyd’s The Wall and Prince’s Around The World In A Day.
And you?
Well, I’ve bought the Postal Service’s Give Up at least 5 times. It’s embarassing, and it’s one of my favorite albums ever (highly recommended,) but somewhere along the way of letting everyone borrow it and me listening to it all the time it continuously gets lost.
I’ve bought the Smashing Pumpkin’s Siamese Dream twice, but that was because I forgot I owned it.
~S&S
Beastie Boys - Licensed to Ill
The Cure - Mixed Up
From my experience, both have an astonishing tendency to vanish. I think the same gnomes that steal all the socks also dig the Cure and the Beastie Boys.
Elvis Costello - My Aim Is True
I bought the album way back when. Then I bought the CD when CD’s came out. Then I bought the Special Edition CD with extra songs when that was released. Then I bought the Deluxe CD with a bonus second disc when that was released. Someday, inevitably, I can foresee myself buying the ten disc box set.
I think Bloodletting by Concrete Blonde wins the award from me. I initially purchased it on record, then on cassette, and am now on my second CD copy.
I’ve got Everything by the Bangles (my favourite record when I was in high school, what a dork!) on record, cassette and CD. Actually, the CD is on its last legs and I really need to buy another copy soon. I can’t possibly be expected to function without a working copy of this album.
Mexican Moon by Concrete Blonde and Grace by Jeff Buckley - I initially bought these on cassette, and have since bought two CD copies of each. I’ve also bought Blur’s 13, The Best Of Nick Cave and the Bad Seeds and Portishead’s Live at Roseland NYC twice on CD. Mainly due to excessive scratching or leaving them in another country.
I really need to be more careful.
MS windows, I bought about 4-5 of themover the years to hopefully get a new version that actually works correctly, but I seem to get the same buggie version because it still crashes. 
Nirvana’s In Utero I’ve bought 3 times, due to losing the other two somewhere in transit.
De La Soul’s 3 feet high and rising: first album I bought, on cassette, lent it out and never got it back, bought it on CD, same thing, managed to pick it up for £3 in HMV a couple of years back.
Gah! people can be such pigs sometimes.
Wimps. I’ve got at least three copies of the majority of Iron Maiden albums, one on tape, one on vinyl, and two on CD. Of course I am a bit strange.
However, I know what the OP is getting at, I’ve bought Gary Moore’s Wild Frontier a number of times. I had it on tape and it got stolen, got it again. Lost it, then got it on CD, and finally after a year of trying to find it, even on the internet, I found the remastered version of it last month in London.
ELP’s Brain Salad Surgery (the one with “Welcome Back My Friends to the Show That Never Ends…”)
Original CD (shoddy mastering)
German CD (better)
US reissue (even better)
Issue with bonus interview track (dispensible - but I bought it anyway).
There were also 2 vinyl copies before that CD craze.
I keep buying Bowie and (cough) Moody Blues CD’s every time they reissue them. Special thanks to Mobile Fidelity Sound Labs for taking all my money.
I’ve bought The Beatles catalogue on vinyl six times (my record collection has been stolen five times). That’s the Canadian catalogue, in stereo and mono, the US catalogue in stereo and mono, the UK catalogue in stereo and mono, plus various and sundry imports from Europe and Japan and Uruguay etc., plus colored vinyl issues and picture discs. And I’ve bought the North American catalogue on 8-track and cassette and the UK catalogue on CD.
I’ve bought “Dark Side Of The Moon” on LP (six times), then on the first CD (shoddy mastering, tape hiss), the second CD issue (NoNoised), the Mobile Fidelity Ultradisc and the latest issue with brickwall limiting and no dynamics whatsoever.
And those are just the first ones that came to mind!
Excuse me while I go flagellate myself…
Excluding everything I owned on cassette and then upgraded with the technology, I’ve bought U2’s Rattle and Hum at least 3 times–which is strange, because I’m not really a huge U2 fan. It’s just that every time I go to listen to it, it appears to be gone.
I’ve also owned at least two copies of the Beatles’ White Album and Ani Difranco’s Dilate.
I bought Talking Heads Remain in Light twice because I lost the first CD of it. Then, about a week after I bought it a second time, I found the original copy.
I’ve bought two copies of Alice in Chains Jar of Flies. I don’t know what happened to the first CD but it is gone, and I still have the jewel case.
My all time grand champion must be Squeeze Singles 45’s and Under. I bought that twice on vinyl and twice on CD. And I don’t know where it is right now. It is like I am destined to not own that album.