Kuala Lumpur sits just three degrees north of the equator and the weather varies very little from month to month: daytime highs around 32°C, nights around 24°C, humidity always high, rain possible any day of the year. There is no real dry season but February to April are the driest and clearest months, and November to January see the heaviest rains, with afternoon thunderstorms most days.
Avoid Chinese New Year (late January or early February) if you want to do business or eat at Chinese restaurants — many shut for a week. Thaipusam at Batu Caves (January or February) is a remarkable sight, with hundreds of thousands of devotees climbing the steps with kavadi piercings. Ramadan brings excellent food bazaars (pasar Ramadan) every evening; Hari Raya Aidilfitri at the end of Ramadan empties the city as Malays return to their kampungs. Late June is the Malaysia Mega Sale Carnival, which fills the malls.
The KL haze, drifting in from peat fires in Sumatra, can be bad in August and September; check air quality before booking.