We've seen private tuition from about $7,000 to $35,000 in the various cities we've lived in.
One thing to keep in mind is that the tuition is just the start. You may also have to pay for uniforms (may be $1000 or more for summer, winter, and sport uniforms), book fees, school sport fees, laptops (several private schools I know have laptop requirements for their middle school and high school students), music - instrument loan and instruction, expensive field trips (how do you say no when everyone is going to the special overnight leadership camp or the big city visit)...it's pretty endless. You may be asked to pay thousands more every year for these things. Everyone complains about extra fees at public schools these days, but I find they are still a pittance compared to private schools.
Then there will be the non-essential add-ons - if the other students all have iPods and cell phones and video cameras and portable DVD players and expensive dance/music/sport/art/etc. lessons and camps and international vacations - you can be sure that your child will be asking for the same things. Even birthday parties become an issue, if expensive, over the top venues and gifts are the norm. You don't have to provide these extras, of course, but the living standard will likely be set by someone in a different income bracket than your own.
Our strategy has been to find the best public schools with the best special programs (gifted, regional art programs) and take advantage of everything offered by our taxpayers. Then we spend fairly freely on private extra-curriculars, theatre, museum and art gallery shows, and travel. It works for us. I know that many people don't have a lot of public options, so it may not work for others.