Gate
This one really got its hooks in me, and I binged 10 episodes last night when I really should have been sleeping. It's a story where a gate (uh huh) opens up in the middle of a busy Tokyo intersection that leads to another world, one of knights, dragons, elves, sorcerers, catgirls, etc. And for some reason, a fantasy medieval army comes pouring through the gate and attacks the shocked civilian populace. Of course, it doesn't take long for the JSDF to mobilize and utterly stomp the invading cavalry, pikemen, and wyvern-riders, who are after all no match for machine guns, armored vehicles, and attack helicopters. The decision is then made to send the SDF through the gate, since it doesn't seem to be closing, fortify the other side, and make contact with whoever is there to try to normalize relations.
It's an interesting series that tries to balance action with intrigue, character exploration, and politics. Naturally, the larger powers of earth (The US, Russia, and China) are all greedily eyeing the prospect of easy access to a new, undeveloped land full of resources to exploit, and even elements within Japan's own government see this development as a way to advance their own agendas. Meanwhile the Lords, Kings, and Emperor on the other side of the gate are at a loss as to what to do against an enemy that seems to wield thunder, fire, and death at even the lowest ranks of their army - those who haven't seen it first hand can't possibly conceive of an enemy that strong, and those that see battle with it first hand usually die quickly in a hail of bullets or artillery. It makes for an interesting "worlds collide" type story.
Of course, it's not without its drawbacks. Some of the female character design choices are so stereotypically japanese-tropish that it almost borders on problematic, particularly where the gothic-lolita demigoddess reaper that gets hot and bothered by combat is concerned. The main character, a minor officer in the SDF, is about as Mary-Sue as you can get. He's a lazy otaku that keeps getting commendations and promotions for doing pretty much what anyone would have done in his situation, except oh did we mention he went to Ranger school? Oh yeah, and I guess we forgot to mention he's special forces, too. And every female ends up wanting him. Etc.
I'm a little less than halfway through, and I looked to see if another season is coming out, but unfortunately it looks like the anime may have run out of source material. Apparently the light novels upon which the anime is based starts wandering off into tangential side stories and whatnot at that point, so there's no more story to draw from, yet, and the anime will have to wait until the author stops doing this "Dunc and Egg" BS and gets back to brass tacks.
But if you're looking for something easy to watch between other major time investments, this is probably a decent choice.