For me the core feature I love about gaming is the notion of being an interactive form of story telling. I enjoy all forms of media but Video games interactivity immerses me so much more.
An interesting example is a comparison from film to game which I have experienced recently. I saw Tron Legacy within the cinemas upon release and while I could see it was on the high end of production value the actual action sequences just weren't engaging me at all and it felt rather boring... Having just played Kingdom Hearts DDD which features an area based off of Tron legacy, I found it to be the most compelling of all areas within the series - Even having not cared much for the source material! The action packed set pieces were phenomenal (One moment had my jaw drop where after a battle I hacked a gun turret which shattered the glass wall it was on, leading to an opening that had you jump down a hue drop to another location where the combat continued!), but I also found myself more invested in the story of that world too.
For me the narrative is key, it doesn't have to always be interactive with choices like Heavy Rain (Though I adore games which allow me too and think it's a great route for the industry to explore!), but I find as the medium requires my input I'm just more invested. Also, I like grande adventure JRPG's which very rarely translate to film very well - Lord of the Rings may be a consideration. But I love going off on an adventure with a cast of characters who each have their own story line and troubles to overcome, I love learning about the characters and seeing their personal growth and understanding upon the trials the adventure puts them through. Plus I often get overwhelmed with the feelings the narrative brings from the sadness of seeing a village wiped out to the warm fuzzy feelings of when a character is triumphant.
I also use games a method to bond with people, lately me and my firend have been playing the whole Kingdom Hearts series in prep for Kingdom Hearts III next week - It's been a thrilling ride which we've often bickered back and forth regarding all the games challenges or convulted story meanings. I personally find it hard to engage with others about many other topics and I find that the industry has plenty to keep me occupied with year after year.