THIS LIST DOES NOT INCLUDE ANIME.
I feel it's important to clarify this, as there are plenty of anime shows that could be considered for this list, and I wanted to make an anime list sometime in the future, so that would be a bit of an encroachment. So now that I've gotten that out of the way, let's move into the other rules of the list.
This list includes shows that both started in and before the 2010s. However, their placement is based entirely on what they've done so far in this decade alone, I will not be considering material that was released before January 1, 2010. I have no distinction between kids shows and adult shows on here, though you will see more adult on this list, as I don't find most kids shows particularly interesting. Alright, now to the list itself.
10. F Is For Family [2015 - present]
This one is pretty fresh on my mind, as the second season was just released on Netflix within the past month or so. If this were counting the first season alone, it wouldn't have been on here at all. I'm a fan of Bill Burr's in your face humor, and while the show can be a bit much at times, when the jokes land they land hard. It's a pretty standard sitcom set-up but with a darker tone; you have the loud and obnoxious dad, a crushed and always-suffering wife, their oldest son who retreats to his music to cope with puberty, the second son who tries to be good but often fails and gets into trouble, and the goodie-goodie youngest daughter who is actually quite vindictive. It plays off these stereotypes in often unpredictable ways, but the true heart of the show returns to the love they all have for each other in spite of their outward unhappiness.
Bill Burr is surprisingly nuanced as the main character Frank Reynolds (who is basically what would happen if Ralph Kramden, Archie Bunker, and Red Foreman were given an R-rated rage outlet), a father who both harbors complete disdain and undying devotion to his family. His outbursts are often very funny, and his introspective moments are equally as moving. It's clear he has a lot of passion for this project, as he has stated Frank is based in many ways on his own father. The show is often shocking and uses this for both humor and dramatic moments. It's absurd and weirdly poignant, and in the end it's a show that is well worth watching if you want to see a family sitcom with a distinctly TV-MA bite to it.
9. Archer [2009 - present]
If this show had ended after 4 seasons, it would have landed much higher on this list, but sadly the quality or the program has started to drop these past few years as they began to distance themselves from their spy agency roots. That being said, the quality of writing and editing in this show are among the best in all of TV history. Much like Arrested Development, this is a show that demands repeat viewings, with layers upon layers of wit and creativity to its presentation of jokes, often utilizing scene transitions to deliver punchlines.
As far as characters go, there aren't any that I wouldn't consider passably entertaining in the very least. I love H. Jon Benjamin's comedic timing as the show's lead Sterling Archer, Jessica Walters is terrific (when isn't she?) as his overbearing mother/boss, and Lucky Yates' mad "doctor" is one of the most consistent highlights of the show's later seasons. The characters are great, the writing is almost always top-notch, and the stories and running gags improve when revisited. The humor has somewhat died out at this point, but it's still a fun watch and always impressive in its execution.
8. Over The Garden Wall 
A fairly rare type of show, OTGW is a fantasy miniseries that only ran 10 episodes and functions a lot like a film broken into chapters. The world this show creates is imaginative, dark, and impressively expansive; a world I wouldn't mind seeing returned to at some point in the future. As far as story goes, this is like a more grounded and narratively focused Alice In Wonderland, one that makes you question the reality of the situations within the show itself.
There are a handful of memorable voice actors here, not the least of which being Tim Curry, who makes a small appearance as the enigmatic Auntie Whispers. The voice cast also includes Elijah Wood as the show's main protagonist, an actor with experience in fantasy worlds (LOTR and Wilfred), as well as Christopher Lloyd who can never make enough appearances if you ask me. While it's a kids show, there is a level of maturity to this that people of any age could enjoy. The story is often simplistic, but imaginative enough to keep you interest. It's about the length of an average movie, so it definitely deserves to be given a look.
7. South Park [1997 - present]
While a few of my favorite individual episodes of the show have been released since 2010 ('Raising The Bar', 'Cartman Finds Love', 'You're Getting Old', the Coon trilogy, etc.), it's the serialization I'm putting this on the list for more than anything else. Their first season trying this out was definitely hit-and-miss ('Grounded Vindaloop' is one of their most ingeniusly crafted episodes ever, for example), but with seasons 19 and 20, the show was able to bring more to the table than ever before by allowing themselves to hit on a topic and focus in on it for longer than just a single episode.
I had almost written South Park off as being irrelevant and lacking in that bite they used to have, but once I decided to sit down and watch through the last few seasons in their entirety, I realized how wrong I was for ever doubting Parker and Stone. While the humor is sometimes weirdly underplayed, the social and political subjects of their parody and ridicule are as on point as ever. While it could be said that covering the 2016 election is an easy target for comedy, the way they handle it is definitely uniquely South Park. This most recent season left me feeling very optimistic for the show's future, as it remains one of the best written shows on TV.
6. Bojack Horseman [2014 - present]
Talk about a surprise. When I watched the first few episodes of the first season around the time it was released, I didn't get it. This show isn't particularly funny, the characters were weird looking, it was incredibly dark...it just didn't work for me. Luckily, I had a friend who was more patient than me and decided to watch it a little longer than me, and his recommendation of the 2nd season being worth the time was enough for me to get past the weird animation and often unfunny nature of this supposed comedy show.
And yeah, it takes most of the first season to develop, but the deeply emotional turns it takes more than make it worthwhile. This is a subtly funny show, but at the very heart it's a tragedy. Bojack is one of the more conflicted characters of the 2010s, a washed up TV star whose fears of intimacy and failure are constantly brought to light as he almost perpetually sabotages himself and deliberately pushes everyone away from him. It's one of the best animated dramas around, and definitely worth watching if you like more heavy adult themes in your animated shows about people with animal heads.
5. Gravity Falls [2012 - 2016]
Probably one of the most surprising shows of the past decade is this one, a Disney Channel original about two kids spending their summer with their weird, greedy uncle in a seemingly supernatural town. I like supernatural things, but I really don't care for (modern) Disney and I've never seen a Disney show I've really liked. Well at least not until I watched this. I was hooked pretty much instantly with this one, as I found its characters fun and likeable, and the stories themselves surprisingly clever and original.
As the show continued I found myself more and more impressed, watching the characters develop and change while the tone of the show began to darken. What started off as a light and entertaining fantasy/adventure show turned into a twisted and apocalyptic epic; and most surprisingly, the transition feels natural. Stan, who starts out like a Mr. Krabs-like greedy caricature slowly is revealed to be far more complex than you would initially think, which pretty much represents the show as a whole. It's fun, creative, and pretty fantastic from start to finish.
4. Futurama [1999 - 2003, 2008 - 2013]
As the title line on the entry suggests, the original run of Futurama was more than a couple years from being eligible for this list. But while I loved the original incarnation of the series, the few seasons it was around during the 2010s were more than enough to put it this far up here. New vs. Old, Futurama is pretty comparable across the board, as the newer seasons put more emphasis into creative storytelling and less on humor, but the laughs are still there. Anyway, I'm not just here to compare the original run to the Comedy Central reboot.
With the 52 episodes from 2010 to 2013, Futurama took risks and offered up some of their most memorable and emotional episodes, not he least of which being the series finale 'Meanwhile', which I consider a top 5 contender for the entire series. This is a show that really speaks for itself and never dropped in quality -- perhaps thanks to its premature cancellation over a decade ago. The ideas and humor stayed fresh, and seeing the show brought back with such energy was pure joy for me. It's one of my favorite shows ever and the latter seasons did not disappoint.
3. Bob's Burgers [2011 - present]
For almost 30 years now, FOX has had at least one massively popular and funny animated TV-14 family sitcom on the air at a time. The Simpsons stayed funny for the first decade, Family Guy was hilarious for a few years, American Dad kind of took over for a bit (though I've never been a fan of that one), and now the ball is in Bob's court. Starting off pretty strong, Bob's Burgers has been incredibly consistent for 7 seasons now, and the best of any of these shows since the earlier years of The Simpsons.
Trying to explain what makes this show good often comes down to Bob himself. Bob is a character that functions as the straight man, unlike the other FOX shows I just named which all have central father characters who are clownish. It's a small change allowing the father to be this character, but after decades of sitcom stereotypes, it feels like a big one. There's a huge supporting cast in this show and most of the characters are funny and varied. Hopefully this show can hold on for a few more years, because as it stands it's one of the best comedies on TV -- and with the absence of The Office, Parks and Recreation, Community, 30 Rock, The League...well, there's quite a hole to fill.
2. Adventure Time [2010 - present]
When I started typing this out, this was going to be my #1. But...well, you'll see. Anyway, when it comes to world-building, character development, and sheer creativity and evolution of story, Adventure Time is one of the most impressive shows I can recall having ever seen. What at first seemed on the surface to be a simple children's fantasy show within a few seasons revealed itself to be far, far more. It may appear to be a dumb kids comedy with fart jokes and excitable lead characters, but as you start to see the layers and changes that occur, you can't help but to become entranced and invested in this sprawling world they created.
I've heard a lot of complaints about Finn (mostly from just one person...you know who you are), but I find him a perfect example of how well developed the show is. He ages along with the show, and with his maturity come all the changes you go through with puberty and the disillusionment of a world that once seemed so innocent and carefree. There's a rich cast of supporting characters, pretty great animation, and a surprising amount of deeply emotional moments and episodes. While I can't say I'm surprised when people say they don't like it, I still feel this is a show well worth watching if you have the patience to watch it evolve. There's a lot more to it than you might think.
1. Rick And Morty [2013 - present]
I've made over 20 posts talking about this show, so it shouldn't be a huge shock that I like it quite a bit. Dan Harmon shows have a tendency to rely far too heavily on references for their humor, but while that definitely plays a part in what this show is about (a lot of the ideas and designs found here are "borrowed" from all sorts of other sci-fi film and TV), Rick And Morty goes beyond those Seth MacFarland type of "do you remember this thing??" jokes and generates humor through the absurdity of the situations and character reactions.
As far as characters go, Rick Sanchez is one of the most entertaining creations of the past 5 years, a nihilistic supergenius with an incredibly pessimistic outlook (I mean, he IS a nihilist, Dude) and a deeply selfish nature. Justin Roiland's voice acting is definitely a little more than slightly abrasive to start, but what he does here certainly leaves an impression and a good deal of comedy comes from the ridiculous nature of his sense of humor. Like I said earlier, I've already written a lot about this show so I don't feel like adding much more. It's one of the most popular cult shows on TV right now for a good reason. It's hilarious, morbid, and utterly fascinating. Now let's just hope the set of season 3 lives up to the ridiculously high standards set by episode 1...