If you encounter the clue “crossword puzzle fan (14 letters)”, then the answer is cruciverbalist, though the word is as much used for the compiler crossword puzzles as the solver.
It seems to have appeared in English in the 1970s. This is the earliest I’ve so far found, about a noted local crossword-puzzle creator, Joseph La Fauci:
Not only does he know a half-dozen languages, he easily can recall 50 words or so to substitute in any one space. That’s necessary for a full-time designer, or “cruciverbalist”.
The Herald (Arlington Heights, Illinois), 27 Aug. 1977.
Another earlier example is the title Compleat Cruciverbalist of 1981 by Stan Kurzban and Mel Rosen, subtitled “how to solve, compose and sell crossword puzzles for fun and profit”). Stan Kurzban tells me that Mel Rosen had come across the word some years earlier in the title of a directory of crossword puzzle notables that was not widely circulated, which may be where La Fauci might have found it.
Whatever its origin, cruciverbalist has spread into the wider language as a result of their efforts to the extent that it now appears in some larger recent US dictionaries and is known fairly widely.
An Oxford graduate, keen cruciverbalist and amateur saxophone player, she was among the first wave of women to be ordained as priests in 1994.
The Times, 27 Jan. 2015.
The word is a modern mock-Latin invention, being a translation back into Latin of the English crossword (using Latin crucis, cross, as in words like cruciform, plus verbum, word, as in verbose or verbatim).
There is also cruciverbalism, for the art of crossword compilation or crossword fandom generally, but that is much rarer.