I second Hallelujah. I saw him sing it in concert here in Oslo this summer, and I had goosebumps and chills the entire song.

I don't know what it's called, but that song with the refrain "You lift me up, so I can climb a mountain". The lyrics are cheesy, the boy band version is awful, but I heard a professional singer sing it solo at a church wedding a few years ago and just burst into tears.

Garden of Gethsemane from Jesus Christ Superstar.

Jerusalem sung by Jessye Norman.

Nothing compares 2 U by Sinead O'Connor.