Rewrite - Asian Kung Fu Generation - Opening #4 for Fullemtal Alchemist
It's basically impossible to find the actual opening so here's the song. This one gives a great feeling to the end of the original show; the desire to rewrite everything they had done. Almost nothing had gone the way they had wanted. The first show did a good job of creating something different than the manga by having the story just get away from the characters. The manga does a great job coming full circle while the first show just derailed. Rewrite was a great theme for the end of that trail.
Again - Yui - Opening #1 for Fullmetal Alchemist: Brotherhood
Again gives a wonderful start to Brotherhood. The song itself is really awesome but the opening explores a lot of the characters and their relationships to each other. It also gives you a good glimpse into how different the animation actually is compared to the first show.
My Story - The Cherry Coke$ - Opening for Giant Killing
This is one of my absolute favorites because when it starts, it's hard to think that it's Japanese. The song and the opening does a great job getting the viewer pumped for the show. It makes you one of the fans in the audience.
Someone Else - Kana Asumi, Saki Fujita and Eri Kitamura - Opening for Working!!
Because why not? The opening is as crazy as the show is. It's ridiculously catchy and is just a fun time.