Well, that honestly depends on which parent you ask. My mom, when she was young, owned an Atari 2600 with her brother. She found it quite fun and such, then moved on from that. Then, she started getting into casual games with the release of the Wii and all of those glorious games like Wii Sports (and Resort) and Wii Party. She bought a DS Lite for herself in recent years in order to play some casual games herself, but she has only one or two games on the system. She isn't that much into fighting, so when I play even something as innocent as Super Smash Bros., she raises an eyebrow.
Funny thing is that in recent months, I've growingly started to become interested in the more Mature games not much because they have guns and such (that should never be a reason to play a game), but because each game has it's own unique style of gameplay and story telling. There are a lot of M rated games that have such detailed plots and awesome gameplay (my only two examples here are going to be the BioShock series and the Half-Life series), but I also play games like Left 4 Dead as well (I'm not much into the "big" games like Halo and Call of Duty, but I do own Halo: Combat Evolved for PC).
Now, I said all that up there for a reason. What I call art (I mean, you're mixing visual styles, music, story telling, etc.), my parents call violent. Now, my Dad, he played games until life really caught up to him. If I can recall, the last game he went out and bought for himself was Warcraft II: Tides of Darkness. For those who don't know, Warcraft used to be an awesome real time strategy game, much like Starcraft. He thinks that video games can be fun, but doesn't think of them as an art form the way I do. This is also the guy who grew up with not an Atari 2600 or a Nintendo Entertainment System, but the ColecoVision (well, technically the Coleco Adam). That is played in my room now, and he and I occasionally play Super Action Baseball and Donkey Kong.
So, my mother doesn't really appreciate the games the way I do, and my dad finds them cool but is too used to the old joystick to try anything new.