Are the Fable games' stories continuous?

they kind of have the same theme, but each is in a different time period. The only thing the same from each game that I can remember is the one narrating lady, at least from 2 to 3 (I don't remember if she was in the very first fable).

I played Fable II thoroughly, and later started Fable III when it came out. As far as I could tell there wasn't really enough related to Fable II to really matter. If you want my true opinion, play Fable II instead and forget about Fable III. Fable III was awful by comparison. Then again, I know that's not what you asked.

I don't think you'll have any real continuity problems if you skip Fable II. I never played the first Fable but greatly enjoyed Fable II, and I think I heard that the first two are more connected.

In Fable 2, in the beginning of the game you find a book that talks about the hero who destroyed Jack of Blades 500 years prior to your current time in Fable 2. That hero is the hero from the first Fable game. By the time Fable 2 takes place the guild has been destroyed and your character and your characters sibling is that last of the "hero blood line" that exists. Teresa (the hooded woman in Fable 2) is the same Teresa from the first Fable game who is also in Fable 3. Through some magical power (or something along those lines) she has lived to the time of Fable 2 and Fable 3. There are small references throughout Fable 2 that connects to the first Fable and also through Fable 3 that connects to Fable 2. At some point in Fable 2 if you purchase all the property in the game you will be crowned "King" of Albion. (Or queen) Supposedly, its never happened to me but ive never bought all the property either. When you play Fable 3, they commonly refer to "The Old Hero King" who died, which is the father of your character in Fable 3. Fable 2 and Fable 3 are very close together as far as time frame whereas Fable 1 would be considered ancient history.