I'm not sure why this is "today's world": growing up in the 80s, I have fond memories of Where in the World is Carmen Sandiego, Reader Rabbit and Math Rabbit, Number Munchers, and the various standalone Speak and Spell devices.
I work in a game company now. We do maybe 70% commercial titles to keep the company busy, but the remaining 30% are educational, philanthropic, or otherwise socially responsible. We've done or prototyped (often for academia or government or both) games targeted at teaching science to young kids, games to teach better practices to third world denizens, and even games to help people with specific health issues.
We also regularly aim our commercial games slightly high for the intended audience, at least in terms of dialogue and story. I like to think of this as the "Rocky and Bullwinkle" phenomenon: you can teach kids very well by having something that is basically fun, zany, and engaging, and throw in more "adult" themes. Almost all of Jim Henson's work falls in this category too.
The lines blur a bit. I'm not sure I like the term "serious games" due to the connotations of "serious"; people play complicated flight or submarine simulators for fun, health-related games are often more effective with fun and/or addictive content, and on the opposite end of the spectrum, children learn more when their zany entertainment has a literate, political, social, or scientific underpinning.
The goal is to prey upon our nature: find something that sparks the desire to explore, to create, to solve problems, or even to compete. Get to a place we'll naturally be intrigued or enjoying ourselves, where we'll naturally want to do more (play more of the game, do more related activities or exploration) and the learning follows.
I don't ever see games taking over entire cirricula. I think you need balance between forms of learning, otherwise you wear things out and you don't form as many associations to strengthen knowledge.
But I do strongly believe that games will make a great part of that particular balanced breakfast. Even for adults concerned with ongoing education and expansion of their abilities; even for reflex training, exercise, or the like.
As an aside, you may be interested in Games in Education; it's a conference held in the northeast each year, which is fairly teacher-centric. Many educators come to speak about their experiences using games to teach -- what has worked, what hasn't, etc. There should be video on the site, somewhere.