What makes a game more interesting or fun to play for children ages 8 to 14+?
Does the age of the consumer play an important role in his/her interest in the game?
What can I put in a game to make it more fun, educational, and interesting to play?
As the communist duck, I'd say there is a huge difference between 8 and 14. Around 12, I started wanting to build something in games, but I was too lazy for Civilization (too many things to understand), so I sticked with Sim City (cheating ; actually, I cheated regularly, not to beat the game, but to build my own story). I used to play the Warcraft "dungeon" levels, just to imagine there were castles. I would have loved minecraft at this age). Before that age, anything "new", with secrets, lots of color, constant things to attract attention worked ; after that, I grew tired of it.
So I'd say the gameplay is the variable, there : it should not be too dense, and be fairly linear (but with "secrets to discover"), before they get twelvish, and then more open-ended, giving more creativity after that. Once again, I'm basing this on my own experience, and I guess everybody is different. And it's likely that each generation is different, so trying on "real kids" would be the best idea.
A note on violence, though : I think it's less violence than power that is attractive to a younger audience. Everything you can't do in real life appeals to the player ; and there is a lot of things kids can't do : drive, have money, own a house, dress as they want, and so on... They're so powerless that every impression of power, influence, will appeal to them. This is why violence is so used in video game, because it is a pure manifestation of power (and this is why survival horror and infiltration are more subtle, and give you another view point on power).
Hope that helps !
Edit : Oh, and a great way to have a good answer would be to go to a local video game store and ask them what they sell to this audience.
Talk with children. Play with children. Then talk with children about their world. Talk about the games. Implement prototype. Test it with children. Iterate ... That will be fun :)
And game should have easy to learn gameplay model and that model should be based on well known "mental model" - you dont have to know physics to know how ball should fly when you kick it. Or how it looks like when somebody jumps.
Side note: the game have to be fun even if you are not playing with children. My cousins loved my game when i was playing with them. But it was boring for them when i was gone.
When I was about 8yo, at our school we had a simple PC game that you played by solving simple math problems (2*4=8) etc to move the pixelated flying man to his targets on the screen. I remember having several hours of fun with that, because the math part was simple enough to become sort of automatic pretty fast. I suspect this was on purpose. :)
The key issue then, in my opinion, is to make the education you wish to pass onto the players stealthy. Kids (the majority) by definition probably feel they get enough education at their school classes already. There are however many ways the education can be slipped into the mix without them noticing. Geometry could be a very fruitful area as it is very intuitive to humans, we just have to sneak in the important aspects and the terms that we wish to pass on. Think trajectories in Worms, things involving Pythagorean theorem that is easily visualized, maybe the distinction between different triangles and how to make use of the shapes in the game etc etc..
When I was 10, I learned the English language with a dictionary at the side, so that I could understand more about civilization 1, but I was able to start to play it because the actual mechanics were very simple. I'm not sure if I qualify as mainstream enough to be a target audience though. But if you want kids to play the game, make sure that the entry skill level is low, even if the game has depth when one digs into it.
At 13 I fell in love with a puzzle game called Atomix, that taught me the structures of many important organic chemical molecules. Perhaps a reason why I'm minoring on chemistry? :) That game was lots of fun and could certainly be further improved to pass on other chemical concepts to the players without them noticing. Perhaps I'll work on this sometime..
So anyways, my hat is off to Sid, and I'm forever grateful for him for sneaking the English language and abridged world history on to me. :)
You will find that education is not a good selling point. You'll never get a 10 year old to play to learn things.
Instead, like Andrei has suggested, violence works well. Make sure it's cartoon and not gore, else it'll just be unsuitable.
Give them something to laugh at, and not their own failure. Children have very little perseverance. Then again, don't make it too easy. ;-)
As for educational, if you can hide that behind a fun puzzle or a way to defeat some evil aliens by solving maths problems, you'll get a lot more interest.
Probably the best thing would be to make a prototype of your game (with nicer graphics) and actually get some kids to play it.
I guess violence will never get boring. Throwing ducks off a cliff seems to be very interesting.
However, when I was 10-11-12-13 I liked Myst-like games, where things had to be discovered.
For most games, you have to learn playing before being actually good at them.
The most important thing (IMHO) is to keep the learning part simple and fast enough. Simple for understanding, and fast to get the player (child) actually involved in the game before he/she quits for another, simple/fast to get familiar (aka 'cool') game or other hobby.
Children will love something that gently tickles their cognitive abilities without letting them know. Any game that has something related to their life (i.e. their imagination) but not too monotonous will be liked too.
An element of anticipation will also be good. A lot of us played games just to get to the next level to experience it, leading to a kind of addiction. Having a storyline or progression that rewards according to the milestones achieved is always great, like access to new arenas/castles, bonus characters, new types of questions or new environment.