None of the existing answers are bad, but I want to add an alternate answer, becuase this is a tricky question. Its very easy to list something that is old and not used or unknown meaning to any regular people. There have even been characters in the past over a hundred strokes-- but if they were even real terms is questionable, certianly not ever true vocab.
So, I want to offer an alternative of actually used modern vocab that has many strokes, and an actually used in old texts big character.
modern use: 齉 is considered by many as the most strokes in a character actually used as normal vocab, a term for a stuffy nose you could use in any sentence ((although
you are way more likely to hear it said out loud than see it written down haha)).
ancient use: would be image courtesy of chairman bao-- a character that wasn't believed to be widely used but has been defined to mean thief ((many big character contenders have no known meaning or use)).
there is no set answer here, since you can easily disqualify certain things to not count. If you only want to count characters in regular education, you aren't gonna break the thirty stroke mark. If you want to include character reduplication you will easily break 100. I personally don't count reduplication, for the same reason if you said “really really really" in english, I wouldn't count that as a different term from just saying really. At least for the duplicate characters we know the meaning of, thats exactly it. Still the original glyphs meaning, just.... duplicated two three four or more times. Compare 木、林、森, very common modern characters in the same principle as those ancient glyphs of 龘 and so on. ((if others feel differently to each their own, it is a tricky question, chinese english or otherwise)).