Well, for me a teary/crying moment vs. a shiver/chills moment correspond to different emotions. But here are my chills moments ~
Wicked ~ Defying Gravity (pratically the whole thing), No Good Deed (Fiyero .... FIYERO!)
Les Mis ~ Prologue (several of the prisoner solos), Valjean's Soliloquy (this is all I have lived for - this is all I have known!), I Dreamed a Dream (with their voices soft as thunder), On My Own, The Confrontation (my race is not yet run!), Javert's Soliloquy (shall his crimes be reprieved? Philip Quast hits the note the best

)
Miss Saigon ~ Why God Why?, I Still Believe (Ellen's solo), Bui Doi, The Fall of Saigon
Phantom ~ Phantom's solo (you will curse the day you did not do ...)
And then my teary moments (I've never actually cried) ~
Les Mis ~ Heart Full of Love and Bring Him Home
Wicked ~ For Good and Finale
Miss Saigon ~ The Fall of Saigon (don't take my love away not now *sniff*)
Phantom ~ Wishing You were Somehow here Again (as sung by Emmy Rossum *nod*)
Can't think of a many other really memorable moments ... but those are mine
Coimhéad fearg fhear na foighde.