There is, to my knowledge, one, and only one, word in Modern English that contains no vowels.
For the sake of clarity, vowels are the letters 'a', 'e', 'i', 'o', 'u', and, when representing vowel sounds, 'y', and 'w'.
As a brief aside, if you don't believe that 'w' can serve as a vowel, compare the pronunciations of "plow" and "snow"; 'w' serves as a vowel in the latter case. Noting that 'w' can be a vowel eliminates "cwm" and "crwth".
There is, however, one word that does not use any vowels or other letters to represent vowel sounds; its vowel is implied. The word is "nth".