I'll exclude retirement visas and work visas - I just want to focus on visas for us guys who have enough money to live somewhere for a while, but who aren't old enough to qualify for a retirement visa.
I'll start the ball rolling...
China: you can get a 6 month educational visa by enrolling at a University and studying Mandarin. Cost of the visa about $1500 for 6 months. But you do get up to 25 hours tuition a week. I've not heard of anyone getting kicked out for non attendance of courses.
Thailand: 1 year ED visa around $800 for a year. This is for a language school, not a University. As of now you also don't need to attend classes.
Malaysia: I got a 90 day visa on arrival, which is pretty decent of them! After spending 90+ days in China and now Thailand I'd say this is long enough to get a feel for a country. I don't know what the rules are but I guess you can do a visa run after 90 days. Given the proximity of Thailand, Indonesia and Singapore this would be very easy.
I'm kind of burning out of Thailand and I'd like to continue in my quest to live in every country in Asia. So I'm interested in hearing about how I could legally stay in Vietnam, Taiwan, South Korea and Japan.
I will then return to my favourite country and spend more time there

Incidentally, "semi-legit" work visas are very hard to get for China these days, and it's pretty much better value to just get an educational visa. Same goes for Thailand, from the prices I've been quoted.