Well... a dragon can speak a lot of languages if they choose to do so, as they are, for the most part, very intelligent and long-lived. It can be generally assumed they speak Draconic and Common, but beyond that, you'd have to ask a dragon, which may prove rather dicey.
If you're talking about Faerie Dragon and Pseudodragon familiars, the former can speak Common and the latter doesn't "speak" but rather purrs, chirps and makes somewhat musical-sounding noises. The D&D Monster Manual says Pseudodragons can "speak" telepathically, but since we don't really have telepathy here, it's more of an empathic link.