Of the animes I've watched, and I've seen plenty. There's a few I'd recommend above anything else.

Kekkai Sensen. It's a crazy fun anime that mixes the mafia motif with the action of a superhero show, topped off with drama and wrapped together in a package that ties everything together nicely. Just when it feels a little slow it ramps up the action or starts the tearjerkers. It's one of the few animes I've watched five times already. 

Baccano. The story presentation was interesting but not for everyone, with drama, intrigue and supernatural action rolled into one it has some of my favorite characters. It helps that I totally dig the mafia scene.

Durarara and it's other seasons. The character development is splendid, toss in some action to spice things up and it never gets boring. 

Gurren Laggan. Mecha anime at it's finest. And a real must see. A lot of it is mostly action but there's a bit of drama in there for character development. But the fights are spectacular. 

Kill La Kill. Skimpy outfits and a plot with some great storytelling, just compliment the over the top action. I bet they could have done just as well without the skimpy outfits and relied on plot alone, but well at least we got plenty of fanservice.