What is the most complex simplifed character?
龖 (dá) from lol.wen's answer has 32 strokes, but I can better that by a bit ;)

齉 (nàng) has 36 strokes, and my favourite dictionary, YellowBridge, defines it as:


  stoppage of the nose; to speak with a nasal twang; to snuffle (as in nose with a cold); snuffling


I should however add that, like 龖, this character is the same in both simplified and traditional script.

Some other ones that appear in Jun Da's character frequency list, taken from a corpus of modern Chinese, include 鱄 (Zhuān, 22 strokes), 襽 (lán, 23 strokes), and 鑪 (lú, 24 strokes).