The weather in Taipei can change drastically in the span of a day. Unless it is summer, you are advised to carry a light sweater or jacket if you travel outside the city. The most pleasant time of year to visit is October-March, when the weather is least humid and temperatures average around 68 F/25 C. At higher elevations the temperatures are about 15 degrees F/7 degrees C cooler. May-September can be rainy, hot and very humid.
The island tends to be humid year-round and receives rainfall during all seasons, particularly April-July. The typhoon (hurricane) season runs June-November, and you should take note of typhoon warnings issued by the Central Weather Bureau, as there can be high winds. Corresponding flooding in Taipei is possible, but not likely.