FF XI and FF X-2 were released around the same time I think in Usa. Final Fantasy X-2 is a direct sequel to Final Fantasy X and made by roughly the same team. Main three characters are Yuna, Rikku, and Payne(new girl character). The game is female focused and according to Play magazine: "Turned the high drama of FF X into Go-go girl power" or something. People don't like it because it seems dump and japanese pop-y and girl focused and different or something, I haven't played it.
After this the main FF team worked on various projects in the FF VII compilation project, which is a series of sequels and prequels and sidestories to FF VII.
FF VII: Before Crisis is a cellphone game released only in Japan(so far) in 2004. I dont' knwo when it takes place compared to FF VII.
FF VII: Advent Children is a feature length cg movie released and the story has some flaws and may be boring, and the music may not be as good, but the graphics are great. It's takes place maybe two years after FF VII
FF VII: Dirge of Cerberus is a PS 2 rpg which is "3rd person shooter" rpg which is a year after FF VII: AC I think. The main character is Vincent Valentine. It's about 14 hours long and has many flaws in all aspects of design but I still like the game. It came out last year.
The other main project in the FF VII compilation is FF VII: Crisis Core, a PSP rpg coming out next spring which has the main character Zack and it's a prequel to FF VII. There are other projects in the series also.
The next main FF game is FF XII, which is made by a different team, the team who did: Ogre Battle, Tactics Ogre, FF Tactics, Vagrant Story, FF Tactics Advance, in that order. It's an all around great game and very popular, but the story needs some improvements I believe.
This fall is FF XII: Revenant Wings, a Nintendo DS real time strategy rpg which is a sequel to FF XII but not as long and huge. The story and theme of the game is like a 180 degree turn. Hopefully this sequel may be better than FF X-2 was.
Also, next fall we are hoping to get FF XIII and FF Versus XIII, both for PS 3. Also, there is FF Agito XIII, for cellphones coming out later. These three games are in the FF XIII universe but not directly related, some relations though. FF XIII is by the main FF team. FF V XIII is by the Kingdom Hearts team. FF A XIII I am not sure who makes it.
I did only basic info on the main FF series, for more info, go here...
http://en.wikipedia.org/wiki/Final_fantasy
http://en.wikipedia.org/wiki/List_of_Final_Fantasy_titles
By the way FF XI is from the same team roughly that made Chrono Trigger, Radical Dreamers, Xenogears, and Chrono Cross I think. After Xenogears or Chrono Cross, some people went to another company and made Xenosaga 1/2/3 and some stayed with Square. I am not sure what the FF XI team has done since, can't remember.
:)
EDIT:
The main team of a game is composed of: Executive Producer, Producer, Director, Scenario Writer, Character Designer, Art Designer, and Composer. :D