Tutoring students or teaching courses online is another possibility for those looking for work at home. This was one of the first actual jobs I'd ever heard of anyone doing at home. It was also one of the first work-at-home jobs I had, with Tutor.com.
In most cases, it's done entirely online using the company's forum or "virtual classroom." There are positions for tutors and teachers in every subject and the student age ranges from early elementary to adult. The pay varies, but you can expect to make anywhere from $8-$10 an hour starting out and as you're promoted to different levels, you will make a little more.
While most companies do require a Bachelor's Degree (in any discipline), some will hire those who have attained a certain number of college credit hours even if they don't have a degree. If you have a teaching certificate, the opportunities are even better! Typically the application process will include a sort of test in the subject and level you want to tutor in.
In my experience, tutoring can be very flexible in terms of schedule, because you basically set your own. The scheduling procedure varies by company, but often you'll either tell them when you're available and they will give you a schedule or you will go into their system and set your own. The downside to this process is that with some companies scheduling is normally based on seniority. That means that as a beginner, you'll be the last to make your schedule and you might not get all the hours you'd like to have in a typical week.
If you enjoy teaching or are looking for a job that allows you to be very flexible with your time, does not require phone work and leaves you with the ability to have noise in your background (no problem with kids, adults or pets at home while you're working), then I recommend looking into tutoring. The school year has just started, so there are opportunities out there.
In addition to Tutor.com, check into Brainfuse, eSylvan and Kaplan. And as always, I urge you to check out WAHM.com if you're looking for any kind of legitimate work-at-home job!