Being incredibly cheap in comparison with restaurant food street dishes make it really hard for a traveler to resist trying them. Although you should always be careful about what you eat and drink no matter which country you are in, there is no need to get paranoid about street foods in Asia. Keep in mind a few simple rules and enjoy your new experience!
The number one rule is Be careful of the water and ice. Though in some Asian countries like Thailand and Malaysia the water is stated to be safe, don't risk your health. Use bottled water, avoid juices and other drinks if water may have been added. If you get a drink in the street refuse ice to be added to it. Though generally it is made of filtered water, hence absolutely safe, you have no security about it. It can be contaminated during transportation and while being broken into pieces - sometimes straight on the ground like, say, in India.
Beware of ice-cream that is sold in the street - it might have been melted and refrozen. The same concern you should have about fruit and vegetables. Peelable ones are the safest. Often some kinds of fruits such as pineapples, melons and water-melons are peeled and cut in front of you - but it's up to you to decide if you want the vendor to do that for you or not.
Shellfish is potentially dangerous. Oysters, clams and mussels even steamed are not safe to eat. So is undercooked meat, especially in the form of mince. Otherwise properly cooked meat is commonly safe as well as other food items requiring boiling, grilling, roasting, frying, baking, so on. It's always better if the dish you've chosen is prepared in front of you rather than pre-cooked hours before.
Among high-risk foods are those served cold and containing raw fluids: coconut milk, fruit juice, sauces and dressings made of fresh fruit and vegetables. Milk-based snacks (usually a great variety of sweets) should be treated with suspicion, especially when you have doubts about their freshness.
Generally stories about food poisoning and food-caused diseases are blown out of proportion. You can get sick even at a nice expensive restaurant. Much depends upon your personal reaction to unfamiliar food. Be wise and don't indulge yourself in trying all kinds of local food at a time. Modify your diet gradually.
And the simplest rule is - take a look and decide for yourself if the food looks to be fresh and attractive. If a place looks clean and well run as well as the vendor appeals to you by neat and healthy looks, then the food must be safe. Choose places full of locals and tourists - obviously they have a good reputation. Even rather ramshackle and unattractive street stalls can give a real banquet to your senses. With little precaution go for street food and sample "a piece of Asian culture"!