It depends on what you consider would be acceptable to you. The most obvious option would be to run a daycare center. Of course that option would drive me bananas. Tupperware and Avon are two other legitimate options. It isn't as easy to make money with these programs as it used to be, and both compete with their own dealers now on the Internet. However if you have a lot of drive and will put in the effort, they can pan out, as can other types of home sales. Most who try these programs don't work very hard at it though and don't make much. 20 years ago I sold Tupperware and could make $4-500 a week doing parties only twice a week. I think it helped that I lived in an affluent area where party averages were higher than normal.
I have worked from home for nearly six years. When the economy was booming all the new Internet business provided huge opportunities and most still have a large, remote workforce. AOL is one of these workhorses, however I don't see the remote opportunites listed on the public Time Warner website. If you want one of those, you usually have to be a volunteer first for six months. Volunteers have access to hidden job boards where AOL and content partners list their opportunities. You have to be with AOL for at least six months as a member before you can become a volunteer.
I found my first telecommuting job that way. I started out as a volunteer in personal finance and ended up as publisher for one of their content partners and later publisher for the larger company that bought them.
When that job ended I kind of fell into an opportunity that resulted in forming my own company. I do PR, writing, media placement, editing and other freelance writing. I also fix computers when those opportunities come up. Now I'm in the process of starting another business. I like reinventing myself every few years.
There are companies that still like telecommuters though a lot of employers still don't believe people will work harder if they can stay home. I managed 75 people that were all remote and they were great workers. Working from home meant they almost never lost time when ill or if they had a sick kid. They also almost always put forth the extra effort when in a crunch because they could do so and not compromise their family life.
Adobe still has a large remote force and they may advertise those jobs on their website. You can also go to Monster and look for telecomuting jobs, but its a bear there because you have to fish through all the ads you know are scams.
Call center work is also available from home and there are legitimate agencies that place these workers WITHOUT a fee to you. I found one a while back, unfortunately I don't remember their name. Googling and patience may uncover one.
I knew a gal who was a concierge for a hotel in San Francisco. She'd been there for years but had two babies in 14 months and wanted to stay home. They loved her so much they set up a satellite dish on her roof and a T1 line so she could do it from home!
My neighbor across the street does insurance compliance.
It seems the best opportunities are often created out of thin air. Take an inventory of what skills and interests you have so you can figure out what might work for you. Perhaps you have an old employer who has things you can do from home or you can consult.
Jobs at home really only exist for those who have a skill that can be applied that way since an employer can't really train someone remotely.
Good luck.