I would just like to ask first of all-- Why is this question always about how many languages one
speaks? Why not ask about how many I can read and write? Because I can read and write a wider variety of languages a lot better than I can speak. I've always been shy about speaking, but I feel comfortable with books and have a great command of the written word.
Native speaker of American English (but can follow the British and other varieties of English too).
I know Arabic, Finnish, French, German, Greek, Hebrew, Hindi, Hungarian, Indonesian, Italian, Latin, Lithuanian, Malay, Persian, Spanish, Swahili, Tajik, Tamil, Tatar, Turkish, Urdu, Uyghur, Uzbek, and Yiddish -- to varying levels of proficiency. I've used nearly all of them in my career, with an emphasis on written language. I can speak many of these conversationally to some extent, but I can read and write all of them. Since you asked about speaking, the ones I can speak the most fluently are Arabic, French, and Italian.
My latest linguistic project was to translate the phrase "I am a woman" into as many languages as possible. I got up to 166. In Thai:
dichan pen phuying kha คิฉันเป็มผู้หญิงค่ะ