First, there are a lot of legitimate businesses that can be operated from one's home. While there are obviously some products and services that can't be sold from a residence, many can.
That said, you seem to be asking about the frequently advertised home based business
opportunities. These are not usually "scams" (meaning an attempt to cheat or swindle), but they're not quite "legitimate" (meaning exactly as represented) in most cases, either. Four things I'd consider when examining advertised opportunities:
1. Can you confirm that the company and the person making the offer are real (verifiable addresses, phone numbers, legal filings with their state, business references such as a bank, etc.)? If none of this information is being offered or provided, and if you can't find any public records about the company or people who are pitching the opportunity to you, there's probably a reason.
2. Is there a real product or service involved? If you examine the initial ad or offering, yet still don't have a clear idea what the product or service is, there may not be a real product or service (at least not one that anyone wants to buy). If it's a good opportunity, there will be something good to sell -- something they're both proud and eager to tell you about, and something you'd be proud and eager to represent. (The companies that designer mentioned above are all examples of this.)
3. Does the profit come from selling the product/service, or selling the
opportunity to sell the product/service? If the business and the person presenting the opportunity has made more money selling the opportunity than they have made selling the actual product or service, the amount of money you can make will be extremely limited (because you'll have to keep selling to new "opportunity seekers" like yourself, just as they did, in order to generate revenue). After all, if there was real money to be made from selling the product or service, why would they cut you in? This question is particularly applicable to Internet-based opportunities and enterprises. It doesn't make sense (to me) to pay someone to start-up "your own web-based business" that sells exactly the same thing as the 2.6 million similar web-based businesses that already exist.
4. Does the business thrive on the same things you thrive on? In other words, will good business revenue come from doing something you enjoy and do very well, or will making money require you to spend time on activities you dislike and would dread doing? (If it's the latter, you may as well have a regular job.)
Hope all that helps. Good luck!