But "Read My Mind" is my favorite The Killers song, for several reasons. Two of them I can express in specific musical terms, and have before.
1) "Read My Mind" does the repeat-the-same-rhythm-with-a-different-melody thing, pretty much throughout. Particularly in the chorus: "The good old days / the honest man / the restless heart / the Promised Land / a subtle kiss / that no one sees / a broken wrist / and a big trapeze" is the same rhythm eight times, with seven different melodies.
2) The chords at the end of the chorus climb chromatically. The chorus progression for the lines above is Gb Db Ab Ab, each for one measure, which is a weird key but a pretty straightforward progression. But when you get to "I don't mind / if you don't mind / 'Cause I don't shine / if you don't shine" it goes to Gb Db Ab (2 beats) A (2 beats) Bb, which is like taking the first couple trips through the chorus chord progression, landing in a familiar spot, and then having your feet taken out from under you as you're dragged to a spot about 15 feet away.
The last thing that sets "Read My Mind" apart is completely ineffable, but I believe it's the most important factor in why I like it so much. "Read My Mind" conveys a feeling of wonder and adventure before pivoting to outright desperation and loneliness. The first three minutes of the song sound like craning your neck to look out the window of an airplane as it passes over a city skyline. Then it takes a minor turn in terms of tone, partially because of the way Brandon Flowers' voice starts to quiver coming out of the bridge. "Woman, open the door, don't let it sting / I want to breathe that fire again" also has that quality of the stubbornness of last resort, like "I'm standing on your porch screaming out / And I won't leave until you come downstairs."
Then you get to the handoff of the melody to the backup vocalists while Flowers (who has this habit in common with Mariah Carey) goes off and does a little variation on the original theme, and by the time the song's quieted down and cooled off, there's a very interesting sensation: That you started out on this journey and went through most of the song with a group, but you're ending it alone.