I'm interested in simplified only for this question - which simplified character retains the most complexity, defined by having the highest number of strokes?
To clarify: I'm after the most complicated character in use on the mainland - i.e. the most complicated character that remains in common use amongst the literate mainland population.
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).
As discussed in the comments for the original post, two candidates are 攀 (19 strokes) and 蠢 (21 strokes).
Both of these are frequent: 攀 is #2439 in a frequency list of hanzi, and 蠢 is #2135.
EDIT: I also forgot 馕 (náng, 25 strokes), which I certainly saw many times on menus in Beijing. The right hand side itself is also a marvel: surely it would have been a candidate for systematic simplification.
as in biangbiang面, specialty noodles that can be easily found on the streets of Xi'an.
Some would say it isn't a real word (even though it refers to a real food).
Some would say there are characters with more strokes (and they would be right).
Some would say that this character doesn't count because the question asks for the simplified character (and there is a simplified version of biang).
But I argue that for the Chinese language learner in mainland China, the 56 stroke biang is the most complex character you will likely come across in real life. Most Chinese language learners who stay in China for any length of time will probably make it to Xi'an. And if you are in Xi'an one of the things "to do" is eat biangbiang面. The noodles are famous because of the character. And the character is famous because of its complexity. So you will commonly find even the unsimplified version there.
The question is ambiguous, but this is the least ambiguous answer I can give.
That's really a hard question to answer. Because there may not be an answer.
龖(dá) (I'm not sure if this character can display in your browser. It's two 龍 together) Means two dragon to fly. And this is announced by an organization called "Chinese Academy of Languages"(I google translated it).
Also there must be more complicated characters such as 龘(dá). But don't pay attention to it, we Chinese ourselves don't know those characters. We only use a little characters(may be 5000? not sure).
PS. I noticed that you mentioned simplified characters, but you must know that not all the characters has it simplified form.
PPS. Another COMMON word 饕餮, mainly used in 饕餮盛宴, which means gluttonous feast, is used very widely and common.
Wikipedia does name a champion:
龘（漢語拼音：dá/tà；注音符號：ㄉㄚˊ/ㄊㄚˋ；粵拼：daap6）字是現時Big5碼編碼當中筆劃最多的一個字，筆劃達48劃（大陆标准48画）。這個字亦是中華民國一般字典中筆劃最多的一個字。除此，該字也是全世界所有常用語言中，極為少見筆劃相當多的雙音節單字。
Although this is by no means a 'simplified' character... or is it? If you absolutely want to write it in simplified style, you'll find that ⿱龙⿰龙龙 is not in Unicode, so you'd be forced to use 龘 anyway.
𪚥 is the most complex unicode Chinese character by strokes (64).
