Howie, As it is nearly Christmas, I am linking to a few of your selections, which I absolutely agree are among the world's most beautiful tunes. You have many additional great choices, My favorite holiday albums ever remain those of Percy Faith's and his orchestra, which my father played very year from when I was very young (back in the mid-late fifties). While I'm at it, HTF friends, have a safe and happy holiday, in spite of the events in the world.
I'm a bit confused about this thread because I took shivers or chills to mean beautiful but inextricably haunting or sad (which is what gives you those shivers), which may just be my interpretation. Not just beautiful which of course can be a happy thing.
Anyway for what it's worth I agree on Harry Nilsson! And if we're talking themes which I take to mean film scores, then I'd say:
Lara's theme from Dr Zhivago
and The Piano by Michael Nyman.
Also, the single, minor piano note at THAT moment in Pixar's "Up", that tells you everything, and breaks your heart.
For songs ones that are haunting, beautiful, heartbreaking and give me physical/literal shivers are:
Village Ghetto Land by Stevie Wonder
Into Temptation by Crowded House
Many songs from Mahalia Jackson