What Zef said. For good and for ill, Dungeons & Dragons (and its predecessor, Chainmail) has largely set the tone for tabletop RPGs of the pencil-paper variety. Not necessarily in the setting department, but definitely in the content (ie, mechanics and what the players to do reach their goals, etc etc).
I belong to an IRL RP group. When I joined, we did 3.5 every week. Eventually, though, the GM got worn out and talked about trying to pull back on the campaign a bit. Seeing a chance (and tired of hearing 'Roll for Initiative'), I stepped in, offering to the group a handful of systems that weren't D&D. One of those systems - CthulhuTech - is the subject of my current campaign, and one I've been running for a couple of years, whose story is supposed to conclude around this time next year.
Now, the systems I laid out, and have brought to the group, almost always have three things in common. 1: they take place in the modern day or later (though I have one major exception to this rule). 2: Experience is handed out at the end of the night, regardless of what happens (IE, you don't need to kill things to level up). And 3: conflict resolution with other living beings is usually solved by punching it in the face. Repeatedly.
Note I said 'usually.' I'm a big fan of solutions to problems that don't require the player characters to be prime-grade ass-kickers. My players know that every so often, I'll throw a problem at them that they need to solve without combat. Usually by telling them that if they screw up, an entire army will be coming down their throats.
The noncombat approach is big amongst two of my players - one because he likes playing the intellectual types that, sure, carry a gun for protection, but they're less the party machinegunner and more the party library; the other because he likes being creative and mixing up his solutions - sometimes you punch it in the face, and sometimes you shank their tires and make sure when he calls the car service the person who picks him up is a "friend."
One guy in my group, who has since moved away (job reasons), came to our sessions for the combat. We could tell. If we spent three-quarters of the night between a handful of fights, he was happy. If we spent less than half the night, he was anxious. And I've only seen him leave the group happy once when it was a pure roleplaying night. He was there to kill things, period.
Back when I first started playing, the phrase 'hack and slash' was often used to describe D&D and its various analogues. Because it so focused on conflict resolution through combat, and not necessarily through other means.
Now, I'm not deriding D&D. D&D did a lot to bring generations of RPers to the table (including everyone at my table except me), and that it has withstood time as well as it has (with a few updates) is testament to it.
But it's not what I prioritize in RPing. Roleplaying is about telling stories: whether it be the thousandth and one rehash of the Hero's Journey (such as Star Wars), or an epic tale of revenge (The Count of Monte Cristo), or a tale about how we can overcome our difficulties and flaws and rise above what we are now (pretty much every spirit-raising movie ever, though I usually cite Remember the Titans).
I am not usually one to do one-off adventures. When I write a campaign, there is always an A plot and a B plot going through it. Sometimes a C plot. And every session, I do something to advance one of those plots. My table has called me three things: "the J Michael Straczynski of the table," "the guy with all the other systems," and "the blind, backwards-shooting archer." (Long story, that last one.)
My group knows that I bring stuff that's not D&D to the table all the time. In my time there, I've brought the following different systems to the table: CthulhuTech; Marvel Universe RPG (NOT Marvel Super Heroes); Final Fantasy RPG (3rd ed); Dresden Files RPG; Adeptus Evangelion; Shadowrun; Exalted; Scion; Eclipse Phase; Remnants; Strike Legion. That's more than 10 different systems (though you could argue that Exalted and Scion are the same mechanics-wise).
And yet, even with all of this, I got looks when I brought the Kickstarter page to the table. I even played the little recorded video. And the best way I can sum up their reactions are in the following phrases: "We'll have to read it when you get your hands on it," and "This is weird, even for you."
I'm not hating on D&D. I'm not. But I am saying we need to have a paradigm shift in what we think of as roleplaying.