There are legit jobs, from my understanding. Many of the jobs are by the word or document and you must be able to type a certain number of words per minute. I have known about five people who tried to get training and jobs of this sort. Only one found a legit job. For the others, the training was more or less a scam, or it seemed that way to me. Several paid quite a lot for the training and then had instructors who tried hard to drum them out so they didn't have to find jobs for them. These all went with services that 'guaranteed' jobs after they finished the training. Only the jobs never materialized or paid so little that it would take years to recover the amount spent on the training. They sure seemed more like scams to me, but I am cynical.
There are quite a few work at home customer service companies if you are looking for work you can do at home. I know that Convergys is looking to hire quite a lot of people most of the time. They are looking for people to do customer service from home. I have heard they can be a good company to work with but I do not know anyone who is currently in their employ.
I used to work in a medical office (years ago!) before all the great software improvements. He had a transcriptionish who would stop by our office about twice a week and pick up cassettes, then transcribe at home. Paid by how many lines. She did this for several private physicians.
The clinic I go to now uses recognition. Software. No one really types it... But the doctor or nurse has to read them for typos and accuracy before it is saved to the patients electronic file.
Nomad - I worked online for about 8 years, medical transcription (MT). Most are legit jobs (though you occasionally get some less than legit folks). Pay was usually per 65 character line (some include spaces, some don't), though some places pay per page or per report - just depends. Straight typing can pay anywhere from 0.05 to 0.09 cents per line. Speech editing (reviewing what voice recognition software has already transcribed) is usually about half that. Most places do have an hourly typing requirement or a daily requirement (editing is usually twice the straight typing requirement). Most also have a turnaround requirement based on the wishes of the client - anywhere from a couple hours to 24. Some places want you to be online at specified times (just like any other job) and others don't care when you work as long as the work is done on time. Quality is a big issue - the companies I worked for required at least 98% accuracy (meaning basically you don't make typos, grammatical errors, or deviate from Book of Standards rules and/or client rules).
If you're looking at MT, they usually require you to have a good knowledge of the Book of Standards (grammatical rules for MT). I learned the skill because I've worked off and on in the medical support field for 35 years, starting back in dark ages when computers barely existed so we typed all the billing forms, etc. I just picked up the terminology along the way. Some of the online schools around now are good, some not so much.
Seems like offshoring and voice recognition has really changed the MT scene in the last 15 years or so, but there are still some companies that will only hire US typists, and voice recognition has it's limitations so there will always need to be a human double checking it (especially in hospital settings).