For some time, I've been hearing rumours (from Arabs, of course) that Arabic has the largest number of words of any language. Recently I found one vector for this rumour: Comparison of the Number of Words in Languages of the World, a poster put together by Azzam Aldakhil which has the merit of at least giving the sources for its figures, namely Muʕjam ʕAjā'ib al-Lughah by Shawqī Ḥamādah, 2000. (In a follow-up comment he gives the page numbers, 83-84.) This poster claims that "Arabic has 25 times as many words as English".
Unfortunately for this claim, if you go to the book cited, what you actually find is a calculation of the number of possible roots in Arabic, without regard to whether or not the root actually has a meaning. Such a count includes huge numbers of unused roots such as بزح bzḥ or قذب qðb, while at the same time lumping together all words derived from the same root; كتاب book, كاتب writer, and مكتب office are three words, but only one root. The result of such a calculation might tell us something about the potential for expanding Arabic, but absolutely nothing about the state of the Arabic language. And since in practice both Arabic and the languages it is being compared to on that poster allow arbitrary long words without real roots, if only in loanwords, it doesn't even tell us much about its potential.Short answer: it depends on what you're counting. If you don't know Lameen's Jabal al-Lughat, get acquainted.