I'm writing an article for my website and will include the best answers.
Video games just sort of replaced television for me. While the average American spends a few hours each day watching TV, I spend some time (not usually quite that much) playing video games instead and never watch television at all.
Games have a lot of advantages over other entertainment. For one thing, they aren't passive, which helps to hold your interest and increases your immersion. Many games involve using eye-hand coordination and problem solving skills, as well, which means they may actually be better for you in some small way than passively watching a show.
A non-gamer probably has an image of a "game" in their head that they think of any time someone mentions the hobby, and that may actually color their opinion of gaming, but the number of game genres is vast. The reality is that there is something for everyone, including many excellently told, nonviolent narrative games. More than a few of these contain stories that put much of Hollywood's storytelling to shame. I mention narrative games mostly because non-gamers tend to watch television, stream movies, etc. and because of these games' general accessibility, which would make them good starting points for people interested in giving gaming a shot.
Finally, just below the surface, I suppose I'm a little defensive. Implicit in these types of questions is a question of morality. Non-gamers tend to ask why you are gaming because they feel that gaming is time poorly spent. They've already made a judgement when they ask the question. You never hear the question, "Why do you watch television?" It's just accepted. The truth is that gaming is just another thing that people do to relax and have a little escape, and it's no worse than other ways of achieving that. Of course, you could always exercise, but that would be awful...