I googled it and so many artists came up that have covered it. I also found three different sites that say Harry Nilsson wrote it, then one that said Bad Finger and another that says Harry covered it and Peter Ham wrote it…ugh…
I was written by Pete Ham and Tom Evans who were in Badfinger.
Oh and the title they used is “Without You”
This site, which sells the sheet music and therefore should be authoritative, lists William Peter Ham and Tom Evans.
BTW, the proper title is “Without You.”
ETA: Damn you, WreckingCrew!
As long as I’ve owned Nillson Schmillson, I’d never paid any attention to the fact that Without You was a cover. It was never a hit for Badfinger, though, while Harry made it a #1. All Music Guide Blurb Here..
It’s only my third-favorite song on the record, though, after Jump Into The Fire and Coconut. 
I was watching some talent show, and the hosts said that the contestant were to sing “Maria Carey’s” Without You.
Which pissed me off. Badfinger wrote the song. Harry Nelson first hit with, and it was in a version pretty much the same as Maria Carey’s later cover.
Nah, it’s called “Ken Lee”.
You beat me to it! 
You know, she actually made it through that round. I don’t know exactly how far she got, but the crowd loved her, as you can see here!
I first heard “Without You” as done by Heart on the Magazine LP in 1978. I may have heard Nilsson’s 1971 version around the time, but it was Heart’s cover that really got my attention. Nilsson was a good vocalist, but that song really takes off with a female voice. I think Heart’s is one of the best versions out there, much better than Maria Carey’s overproduced take.
Here’s the original Badfinger version. It’s terrible. Even though they wrote it, they didn’t see its inherent power and emotion. The chord progressions are all wrong, the vocal phrasing, everything. If you didn’t know that they had written it, you’d think they were a bunch of rank amateurs ruining a great song.
It took Nilsson to bring out the song’s potential and turn it into the torchy rock anthem it has become. I haven’t done exhaustive research, but it seems as though every cover of “Without You” since then has used Nilsson’s arrangement, not Badfinger’s original.
It’s an interesting example of how the creators of a work of art aren’t necessarily its best interpreters.
Oh, yuck!
Lest anybody get a bad Badfinger vibe, I offer this soothing balm of the power pop greatness that Badfinger (at least sometimes) was…
I don’t have it in front of me right now, but the liner notes to the Best of Badfinger album mention that they thought that Nilsson really did the song justice, and that they loved his version. Also something in there about them not having the guts to get as emotional as Harry does with the lyrics and regretting it when they heard his take.
I heard Nilsson’s version first, and while I find it a bit overwrought, the Badfinger take really does sound like a demo in comparison. A case where the cover becomes the definitive version.
I don’t want anyone to get the idea I’m dissing Badfinger in general. I like a number of their songs, particularly “No Matter What.” I remember the first time I heard one of their songs, thinking it was a new Beatles song. At first I thought they were ripping off the Beatles sound, then I found they were, in effect, protegés of the Beatles.
I’ve just read the entry on the band in Wikipedia. Interesting, but tragic. I remember hearing someone claim that the lyrics to “Without You” were on a suicide note. Not true, obviously, but a somewhat understandable conflation of the feeling of the words with the fact that both its authors later committed suicide.
What’s even worse is when it won song of the year via Mariah Carey’s version, and you think the two deceased will now get the recognition they deserve, the other two assholes from Badfinger go up on stage like they had any contribution to the writing of the song.