Red Hot Chili Peppers/Tear Jerker

The most emotional song on One Hot Minute is appropriately titled "Tearjerker". It's a eulogy song to Kurt Cobain, who Anthony Kiedis held a lot of respect for. It's beautiful. You would not suspect it to be a Red Hot Chili Peppers song at first, but Anthony's distinct voice gives it away. Dave Navarro's playing is superb -- and can serve to make you sad, or provide an uplifting sense of serenity to the listener.
"My Lovely Man", Anthony Kiedis' tribute to the bands original guitarist Hillel Slovak, who died of a heroin overdose.

"Just in case you never knew
I miss you, Slim, I love you too
See my heart, it's black and blue
When I die I will find you..."

"Wet Sand". Especially the beginning.
"Death of a Martian", a tribute to Flea's dog, who died while they were recording Stadium Arcadium.
Then there are "Under the Bridge", "Dani California", and "My Friends".
"Brendan's Death Song" was written in the first jam session for I'm With You, which took place immediately after the band had found out that the man who had not only helped get them famous but had also been a lifelong friend--Brendan Mullen--had passed. Thus started a somber jam session which became Brendan's Death Song, one of their most poignant requiems yet (and given their tendency towards requiems, this says a lot).