Southeast Asia is typically hot and sticky for most of the year and it also rains a lot owing to seasonal monsoons effecting different parts of the region at different times. The whole region lies within the tropics, with Singapore, Malaysia, Indonesia, and southern Thailand being closest to the equator and thus the hottest, while Vietnam, Laos, Cambodia, and central and northern parts of Thailand are slightly cooler.
Most of Southeast Asia remains hot and dry between April and May, with monsoonal rain between June and October, and cool, dry winds from November to February. Malaysia, Brunei, Indonesia, Singapore and the Philippines basically have a wet season (in winter) and a dry season (in summer). Temperatures can hit the high 30s in the dry and down to around 25°C in the wet.
November to February
This is the most popular time for tourists, since most come to escape the winters of Europe and North American, thus hotel rates and crowds are at their worst. For Thailand, Malaysia, Burma, Cambodia, Laos and Southern Vietnam it's also coolest and generally rain free. The east coast of Southern Thailand parts of Malaysia do suffer unique moonsoons at this time, and tropical downpours are common in Singapore. Contrary to other countries this is also the wettest time for southern and eastern Indonesia, including Bali. The Philippines also gets the tail end of its wet season towards the end of the year, while Northern Vietnam is decidely chilly and often misty.
March to June
Generally the hottest time of the year for central Southeast Asia when the tropical heat can be unbearable, especially in Thailand, Malaysia, Cambodia, Laos, Burma, Southern Vietnam and Singapore. Haze affects the Northern reaches of the Southeast Asian interior were seasonal burning is a problem, making sightseeing disappointing, and it can get very dry, although storms bring heavy rain in May. It remains dry through most of Indonesia and the Philippines during this period.
July to October
Considered the 'Wet Season' for much of the region, these months are characterised by torrential rainstorms in most countries where several heavy downpours in the space of day are not uncommon, it might be cloudy for a week, or lovely and sunny with a few threatening cumulonimbus clouds in the late afternoon. A patina of green rice paddies dominate the landscape, and the Philippines suffers particularly from heavy storms and ocassional typhoons. By contrast it is mostly dry across Indonesia with the rains arriving in September on Sumatra.
Northern Southeast Asia
The more northerly climes of Thailand, Laos, Cambodia, and Vietnam generally have hot, wet and dry seasons with the cool (dry) part running between November and late February. The wet season in these parts of Southeast Asia are also a lot milder than further south where rain is generally short-lived and days can still be pleasant.
In mountainous areas of northern Thailand, Vietnam, Burma and in Laos, the winter months between November and March can get decidedly chilly and it is worth packing accordingly if traveling during this time.
Tropical Southeast Asia
Most of the rest of Southeast Asia, including Singapore, Malaysia and southern Thailand, remain hot and humid year-round, with temperatures around the mid-30s and with high humidity. The only escape is to head for the high altitude regions of these countries, although Singapore suffers in this respect as it is pretty much flat.
The heat in Southeast Asian cities during the hot periods can be excruciating as there is a lack of air flow, plus the heat and pollution from the traffic exacerbates things. Wearing light cotton clothing during these times is a must and, luckily, cheap clothing is widely available.
On the pollution front, most large cities in Southeast Asia, with the exception of Singapore, have high levels of pollution. This problem is made worse in Malaysia, Brunei, and Sumatra in Indonesia from the haze created from 'slash 'n burn' forest fires in the dry season (May to October).