It definitely should be free until you're done with high school, no matter who you are and what your potential might be. In many countries, you need, at least, a high school diploma to have a decent job nowadays. High school is almost necessary if you want to live a normal life! Only very lucky or very resourceful folks can manage to live well without high school.
I also think that people who dropped out of high school and who now want to get their diploma should be helped financially. People without a high school diploma usually go back to studying because they need the diploma in order to get a job. Maybe we could make them pay one half of the cost - not all at once, maybe monthly, and once they get their diploma, they are reimbursed by the state who ends up paying everything in the end, just like normal high school students. Using the carrot technique could be beneficial since these new diplomas could mean new jobs. And of course the person would have a better life, crime rates might drop too...
After high school, and speaking about funding, I think two major elements must be taken into consideration:
1- The student's potential. If the student performed very well during high school ( and later ), the state should do everything to make him/her reach his full potential. It would be a shame to see a brilliant mind not being able to reach university because he/she doesn't have the money. The better you are, the less financial pressure you should have.
Of course, you'd get a different kind of pressure: the pressure of constant success! But hey, that's part of life.
2- The student's and the parents' financial background. If the student has rich parents, then I believe they should pay for a significant percentage, if not the entirety of the costs for the student's studies if the student wants to go to college and university. On the other side, parents who live in poverty should be spared from paying. The amount to pay would depend on how rich you and your parents are, and I guess it could also fluctuate, depending on the country's gross domestic product and other variables.
One problem we could have is seeing a poor student using the system to study for many years at the expense of the state. I think an age limit could prevent this. Once you reach a certain age, you have to pay more in order to keep on studying.
Another issue would involve parents not wanting to pay for their children's education. I think, once again, that an age limit could be good for this. If you are 45, I don't think it's your parents' responsability to pay for your studies anymore. But if you are 22, and if your parents are financially capable of paying for your studies, I think they should, even if they don't want to. Maybe 25 years of age would be a good limit?
So, yeah... I voted Yes, but I guess I'm between Yes and No. :P