My favorite is “Without You.”
A great song too, in fact it has a very similar piano riff to begin the songs.
I went to this site, and just saw that Randy Newman actually wrote Remember, which surprised me—though Randy Newman does have a great talent for writing interesting, memorable tunes.
Without You was written by Peter Ham of Badfinger, but Badfinger’s original version wasn’t a hit. Nilsson made the song famous and did a great job with it.