I used to get it more frequent but these days it's pretty rare that a song will get me to a state like that. I LOVE when it happens though, at those times I appreciate how powerful and wonderful music can be that can convey a feeling like that.
What's interesting is what actually makes you get that feeling and for me it's very random and can be everything from a section in a song, a certain melody, a chord progression or just hearing vocal harmonies in a band setting or A cappella in some form. Just hearing someone with a beautiful voice can be enough for me.
I do think that for the most part that feeling comes from harmonies, chord progressions and melodies that you've heard before or feels familiar in some ways even if it's a song you've never heard before you can still get it because when you hear it you get a feeling of comfort and pleasure. As someone mentioned nostalgia can also a big part, I think.
To mention some random occasions,
crank this up and you might get a few goosebumps like I did the first time I heard it, make sure to stick until the end. Hearing my country's
national anthem or a nice arrangement of Star Spangled Banner like
this or when a giant crowd sings
Rule Britannia. I think the most recent was when I heard this wonderful rendition of
Nessun Dorma by Jonas Kaufman.