I tried to take a head count for the number of different aliens in the reception room at Journey to Babel on the assumption that every Federation member sent a representative. Then I added a few planets (the Xindi and the Bolians, for example) that were probably members but just weren't present at the reception for some reason.
I figure the Federation would have sixteen full members (homeworlds) a few dozen affiliate members (colonies, allies and protectorates). I also envisioned the Diplomatic Corps being a lower house of the Federation assembly with legislative powers of its own; you don't need to actually BE a member of the Federation to sent a representative, just be a government recognized by it (similar to the U.N.). That is meant to explain the presence of Klingon and Romulan ambassadors just sort of hanging out at Starfleet headquarters in STIV, V and VI; they're ambassadors from Qo'nos and Romulus appointed to represent them in the Federation diplomatic corps.
IOW, not everyone who interacts with the Federation are actually PART of the Federation, and not every alien who serves on the Enterprise is actually FROM a Federation member world.