Jonathan Young and LeeandLee did an AMAZING English cover to the Attack on Titan. Here are the linksA lot of people love Death Note's OP1 & ED1 (and they're fantastic), but this is the one that really stuck with me:
Monster's ED is fantastic at setting the mood, if you ever watch it, make sure to watch the ED every episode.
This is probably the catchiest OP I've heard this year:
This opening pretty much put Attack on Titan on the map, I know so many people who were sold on the series the moment they saw it, so good at establishing the selling points of the series, and with a kick-ass track too.
The second Shiki Opening is the best one of the two in my opinion.
Also for reference here is the Japanese Counterpart ED to Monster - "Make it home"