Every time I despair about the public opinion of games, I remember how people viewed film in the 1930's and stuff like that. It takes generations for a new medium to be taken seriously, even under ideal circumstances.
When I try to explain why I love games, I explain how I view electronic games as the natural progression of various forms of art and entertainment, and how it is fascinating to observe a medium growing and changing visibly within the space of a single year. I compare current games to the black and white films of the early 20th century, and explain that even if there are a lot of bad games that waste time, that's only because the basic vocabulary is still in the process of being made.
Then, when they start to glaze over, I mention something about how video games are like movies "before Citizen Kane and stuff" and they suddenly get it.