"Come As You Are", with the lyrics "No, I don't have a gun". Oh Kurt...
"All Apologies". The final part with the distorted guitar and Kurt singing "All in all is all we are..." is choke-inducing at least.
The MTV Unplugged in New York album also has tons of this.
On that note, Kurt Cobain's rare "Do Re Mi" demo, on the WTLO box set. It is one of the last songs recorded before his death, and while a lot folkier and more upbeat than his earlier work, it still manages to be tear inducing.
"Pennyroyal Tea" can really be depressing (it helps if you pay attention to the lyrics knowing Kurt suffered from gastritis and drug addiction).
"Serve The Servants" A song about Cobain's family and childhood. William S. Burroughs, who had collaborated with Cobain, reportedly said that Cobain was already dead upon hearing the song.