Oooh, songs that shiver me timbers... I would have to say Dancers to a Discordant System by Meshuggah, The Art of Dying by Gojira, and 10,000 Days by Tool.
Dancers to a Discordant System is also probably my favorite song of all time (sounds a bit dramatic though). Simply an amazingly written piece of art that in my opinion excels in the musical aspect as well as in the lyrical aspect. This song includes I think something like 9 different polyrhythms (in 9 minutes), and manages to deliver a particular haunting and penetrating tone. Additionally, the lyrics in this song are just incredible. Such powerfully delivered concepts and ideas... The whole song gives me chills just from its concept itself, but if you still want specific parts then it would be: 3:54 with "Humbled, brought to our knees - by the weight of our own guilt", the entire section of 4:56 - 5:25, and then the entry to the breakdown in 5:26.
The Art of Dying gave me so many chills the first time I heard it, especially in "I try to keep an eye open, and I realize - I haven't closed my eyes in a long time" in 2:36.
10,000 Days is one of those meditational songs that you never want it to end ('cause Tool). The chills part kicks in at 5:22 with that harmonized voice (?) that immediately makes me want to burst into tears every single time again.