You should listen to the full first movement of Beethoven's 5th Symphony. It's one of the most popular pieces of music in history, and for good reason!
I can't believe I never listened the whole piece. It has been an awesome experience! Thank you!
For a more modern one, Apocalyptica's Nothing Else Matters (the Official Video on YouTube is the exact version) is one of the most memorable frisson experiences I've had in recent years. After I first heard it while dancing I listened to it for like a week straight and got frisson at the climax basically every single time.