Awesome / Florence + the Machine
Her performance at the MTV Video Music Awards.
Also her Brits collaboration with Dizzee Rascal. His song "Superstar" flows perfectly into "You've Got The Love".
Also, her performance during the Oscars, even if it wasn't one of her songs. THE VOICE!
"Seven Devils" live at her latest tour. See "Seven Devils (Live at York Theatre) HD" on Youtube and prepared to be blown away by her vocal skills and how the song has so much... more to it live.
"No Light, No Light" performed live at the 2012 Brit Awards, complete with Incredibly Long Note.
Her live shows in general, taking requests from fans, goofing off, big vocal moments, the moments when everybody's singing along which is rather often.
Getting picked out of all the other obviously vengeful songs for the finale of Revenge using their song "Seven Devils" definitely gets an award.
The mindblowing, utterly insane last two minutes of Mother. It has fuck-all to do with the rest of the song, or album, or her career, but it's undeniably exhilarating. See the Gainax Ending trope for details.
Doing a cover of Ben E. King's "Stand By Me." For one of the most anticipated games of all time. Let it sink in.