This poignant, pretty tune was one of the few composed by George Harrison in the early recording career of The Beatles. (Through most of their years as a band, Lennon and McCartney largely viewed Harrison as a junior partner. I remember reading recently, Lennon and McCartney briefly considered including George in their songwriting team. But they rejected the notion, probably so that they could keep writing royalties to themselves. This left the youngest Beatle alone in his composition efforts which, in the early going, according to Beatles producer George Martin, were painful, as in, not very good. But there's nothing wrong with the quality of this song.)
I Need You appeared as part of the soundtrack of The Beatles' second film, Help. I love the sparseness of the arrangement, typical of the band's early work. The arrangement, of course, includes background vocals in which Lennon and McCartney, as usual, harmonize beautifully. (Their harmonies are among the things that set The Beatles apart from their contemporaries. To this day, their harmonies on Abbey Road, their last studio LP, though Let It Be was released after the former project, blow me away.) The Beatles' version is the first video below.
The version by Tom Petty and the Heartbreakers comes from the tribute Concert for George, which took place in 2002. If anything, Petty's version is even sparser than the original. Petty's voice isn't as "pretty" as George's, but somehow by its relative thinness, conveys even more of the poignance and plaintiveness of the song than Harrison managed when he first recorded it at the age of twenty-two. Generally, I'm not a fan of cover versions, but this one is beautiful and truly affecting.
Please remember how I feel about you
I could never really live without you