I homeschool my children. I didn't think this was considered unusual or negative, but mentioning it elsewhere on Reddit has shown me there is a lot of misinformation and hostility toward it. So, I invite you to AMA.
I am a former public school teacher and I now homeschool my daughter (13, 8th grade) and my son (5, kindergarten). This is our third year.
I homeschool because I want my kids to have an experience-based education. We use textbooks for things like math, science, and history. Both of my kids are avid readers, writers, and artists. I teach writing using my own curriculum to my own children as well various groups of kids for pay (which is how I fund our travel). I send them out for music, art, and PE classes, as well as science lab classes. But the basis of their education is in experience, and we spend a lot of time outside, in museums, speaking with experts, and exploring places away from home. This year, we've been all over, including places within our our state, as well as across the country and overseas. I'll link to two of my Facebook albums, if that's allowed, to show you some of what we've seen and done...the first one is from our Oregon trip, where we spent a month, including a week on the road studying geology, and the second is from our Virgin Islands trip, where we lived in an eco-camp that runs on renewable resources and where we worked with scientists and studied the coral reef. My daughter is still participating in an ongoing public outreach project to educate people on the reefs and their importance.
EDIT: Removed albums because of morons.
I think that's enough fodder to open with. If you have any questions, I'm happy to answer! I think there are a lot of myths out there about homeschooling, especially about socialization, and I would love to dispel some of them.
EDIT: I forgot to mention that we do not homeschool for religious reasons. I am an atheist, my husband is a Muslim (pretty much only culturally, though I think he does believe in God), and my kids are free to decide for themselves.
EDIT again: This is exploding, and I don't think I can possibly get to all your questions! I'll write a little more on the most popular areas, so that maybe some questions will be answered up-front.
Socialization: My kids do something with other children every single day. The have art class, gym class, music class, books clubs, literature circles, various co-ops, and one-off special event type things regularly. Parents organize gatherings of kids similar in age on a regular basis. We belong to a community of homeschoolers that is made up of over 150 families in our area. Three hundred children in these families participate in various activities offered by the group. All kinds of kids, all different ages, with all sorts of personalities and abilities/disabilities. There are some they love, and some they don't like, and they deal with it all effectively.
Sheltering: Both of my children are away from me quite often. I do not shelter or smother them. They learn from other people, and they have their own interests that I'm not necessarily a part of. Hell, I hardly ever see my daughter on the weekends. I'm sure she'll have plenty of opportunity to get into the usual trouble and make her way out of it...hopefully not at 13, but I have no illusions about what's coming up in the next few years.
Money: The way we homeschool is kind of expensive, with all of the travel and whatnot. The money I earn working at my part-time tutoring business goes directly toward their educations. We are not wealthy, but we find ways to do what we want to do. It does not have to be expensive though, so to those of you who stated you are considering homeschooling, please don't factor that into your decision.
Religious vs. non-religious homeschoolers: We are secular, as I stated above. I know no homeschooler personally who is a fundamental religious homeschooler, though I know they do exist, and did exist in much greater numbers in the past. The demographics of homeschooling are changing drastically, and I think it's important for us all to note. I believe that keeping your child at home to seclude them and indoctrinate them into anything is flat-out abuse. I hate that what I do is mixed up with this other kind of homeschooling, and that's why I decided to do this AMA...to give another viewpoint.
I'll be answering more questions later, but my fingers need a break right now. Thanks for all of your responses!