Mugen said:
They're from separate series, though the one on the left does still have that sort of action.
Left:
Mio from
K-On! with a Sword. She doesn't actually wield a sword in K-On nor does K-On involve anything actiony or epic. It's a slice of life show about cute girls in a cute band doing cute things with little to no conflict, so I'm going to assume since you're interested in swords, that isn't the show for you.
Right:
Saber from the
Fate Series, specifically in this case from
Fate/zero. It's a very action based series (especially Fate/zero) so I'm going to guess it's within your tastes, although the fantasy components may seem convoluted, especially how they do an info dump of most of it in the first episode. Fate/zero is a prequel to Fate/stay night, which is more romantic than Fate/zero and overall has less of teh awesomesauce action desu, but grounds you into the universe better, so I suppose you could watch Fate/stay night if you want to have a better understanding of Fate/zero (though even then, you will have a few surprises in Fate/zero that were never touched on in the Fate/stay night anime). Fate/zero is a two season series that only finished up its first season a few weeks ago so you can go ahead and watch the whole season and then cry about the cliffhanger like the rest of us. Second season comes back in April.
To take a tangent from the OP, I'm a little annoyed by how non-anime watchers aren't really contributing to the topic as much as bashing on it. This is the Escapist, not /b/, wise-up.