I think there are 16 if you include Final Fantasy Tactics and Final Fantasy X-2.
It's really not too late to play any of them. Assuming you have a PS1 still, you can find pretty much all of them for cheaper than any current new games on the market. Also like mentioned, it's not like one continuous story line, each game is stand alone. The games usually have some common characteristic that make it "final fantasy-y", but the games aren't sequels. Only X-2 is a sequel. For example, a lot of the games are played in the same worlds, or have similar "jobs" or "classes", or themes, or recurring characters like Cid.
If you really want to get into Final Fantasy, I'd say to test the waters with either FF7, FF8, FF9, or FF10. In general those are the fan favorites, and they are the least "dated", so to speak. Out of those, I think that FF9 is the most true to the series, so maybe try that one first. It is the best feel of what a FF game should be, like it's the end all be all culmination of the FF world in my opinion.