The first was a crafts business, which was easy to market but difficult to sell at the right price to make a reasonable profit. Although this is a business that is extremely personally fulfilling, it is difficult to hear people say things like, "I could make that for half the price". There is a difference between hobbies and crafting as a business - you really have to be both business person and artist to pull off a crafting business.
The second was a freelance graphic design business, which brought in a good part-time salary on part-time hours for 4 years. I would still be doing this today if I was still interested in the field. Freelance service businesses offer the ultimate in flexibility yet are great for staying connected with others who have remained in the workforce. If you plan on re-entering the workforce once your children are grown, I highly recommend this business model. If, on the other hand, you want to stay at home and grow your home business into a larger company, you have to be willing to hire out work and become more of an account manager and sales person with this business model.
My third is an internet home based business, in which I combine blogging, writing, and affiliate marketing to drive revenue and new business opportunities. Although this is a popular and attractive idea, making money online is NOT easy and there is a steep learning curve. On the flip side, scaling an online business is much easier than in a service-based business. This is because you aren't billing time, you are monetizing web traffic.
Lastly, there are far more ways to start a business from home. Entrepreneur.com has an extensive collection of guides on their SmallBizBooks.com site. Just keep in mind that you had better pick a business that you are very passionate about, because running a business is hard work - there will be days that your passion is the only thing that will get you through the work you have to do!