First on your list should be an open mind and a sense of humour. Don't come with too many preconceived ideas about what Southeast Asia is like, as media and friends' experiences have a habit of distorting reality.
Otherwise, bring as little as possible. If you forget something, you can probably buy it once you're on the ground travelling. Take enough padlocks for every double zipper to stop wandering hands and lock up your sacred belongings, even in your hotel room.
Essentials are a swimming costume, a day pack, a raincoat/umbrella in rainy season and some warm clothes if travelling in October to December, as some areas get cool. You will only need a couple of changes of clothes as you can get washing done anywhere cheaply. Remember dark clothes do not need to be washed as often, as long as you do not have a BO problem or sweat profusely. Sandals for when your hiking shoes are too hot can be bought cheaply in-country, although large sizes for women are hard to come by.
Take snorkelling gear or buy it on arrival if you plan to spend a lot of your time in the water. Alternatively put up a notice looking for gear from someone who is leaving. A tent for camping if you're a national park buff is a good idea, as is a compass. You might like to bring compact binoculars too if wildlife is your thing. A good map is also handy.
Take earplugs for when you're stuck in a noisy room or want to sleep on the bus. Take a mirror for shaving, as often budget places won't have any. String is very handy for hanging up washing. Travel scrabble can be great. Cigarette papers can be difficult to find, except in tourist centres. Climbing shoes for rock climbing are useful as the region has some of the best cliffs in Southeast Asia.
A spare pair of prescription glasses or contact lenses plus a copy of your prescription is a good idea. Bring a book you're prepared to swap. A personal music player is great as a huge range of cheap music is available everywhere.
Into the toiletries bag throw sun screen and insect repellent. Mosquito coils are also a good idea. A small pocket size torch will come in handy when the electricity goes out or for investigating caves. Condoms, of course. Passport photos come in handy for visas.
If you plan to travel long distances by motorbike, purchase a good quality helmet. Last but not least, pack your stuff in plastic bags to stop them from getting wet, especially when travelling in the rainy season or on boats.
Aside from the above, the following are essential:
Passport with minimum 6 month validity left
Blood donor/type card
Details of your next of kin
Prescriptions for any medication you require. Most chemists will sell medicine over the counter without a script, but if you are searched by immigration it's good to be able to show you require what you're carrying.
A second photo ID other than your passport
Planning well is an integral part of getting the most out of your trip. Be it picking the right backpack, the right vaccinations or the right country, the simple decisions are often the most important.