I've backpacked around Thailand, Laos and Malaysia a number of times since 1995, each time for periods of between 1 and 4 months, and from personal experience I would recommend you take as much money as you can afford and if possible, have access to more if required.
Obviously it depends on what you want to do when out there: doing little else than sitting in a hammock on your beach hut porch for a month reading books is going to be cheaper than taking trips, seeing the sights and travelling to different places. Of course you 'can' do it on the cheap, but there's no point going all that way and not being able to experience it properly through lack of funds. Worrying if you can afford to do stuff 'and still eat this week' can be pretty soul destroying... I've done it.
The best advice I can give is do a bit of research: decide on a few things you know you'd definitely like to do/experience in each Country, find out current costs and budget accordingly. Also look at/sign up to some travel/backpacker forums and pick everyone's brains... they'll be no shortage of advice from people who've just come back, who will be more than pleased to pass on information...
Have a look here for South East Asia:
http://www.khaosanroad.com/