My favourite band is Muse. So many of their tracks "move" me. I think it's the full sound they manage to get.
Their current single (Madness) is one example. The bit towards the end (when they come in with the "proper" instruments, rather than the "synthesised" instruments at around 2:50 in the below link) literally sends shivers up my spine.
Now, I have finally seen the light
And I have finally realised
I need to love I need to love
Come to me, trust in me...dream. Come on and rescue me
Yes I know I can be wrong
Maybe you're too headstrong. Our love is...
For me, the fact that they play their songs extremely well live is a massive factor too, as seen
here on Jools Holland.