You're asking a great question that often comes up in word puzzles!
While "committee" has three double letters (mm, tt, ee), they are not consecutive.
The most famous and often cited English word that has three consecutive double letters is:
BOOKKEEPER (oo, kk, ee)
And its related forms:
BOOKKEEPING
BOOKKEEPERLESS (and other less common derivatives)
There are very few, if any, other widely recognized unhyphenated English words with three consecutive double letters. Many other words might have three pairs of double letters, but they are usually separated by other characters, like "committee" (c-o-mm-i-tt-ee).
So, "bookkeeper" is the prime example when discussing words with three consecutive double characters.