Awesome Music: The Obsessive Devotion, Fools Of Damnation, Martyr Of The Free Word.
The Classical Conspiracy. All 144 minutes of it.
Pretty much any of their title tracks and/or grand finales, at least within the confines of their respective albums. Comparing The Phantom Agony's title track to, say, Serenade of Self-Destruction might be a little unfair given that TPA was them just getting started, but when you hit the last song of an Epica album, you know you're in for a big finish and a hell of a sendoff.
Epic Riff: "The Obsessive Devotion", "Guilty Demeanor", "Internal Warfare", "Fools of Damnation", "Monopoly On Truth" and many more.
Heartwarming Moment: "Our Destiny" is a beautiful song about Simone and Mark not quitting the band because they weren't meant to be.