okay.
ff1 has 4 dungeons that each open up upon the defeat of a fiend. one for earth, fire, wind and water. it starts off with 5 floors and each dungeon adds 5 if i remember correctly. they are somewhat randomly shuffled around for each run through, but the layouts for each individual floor is the same.
each dungeon has 4 bosses; and uses bosses from other ff games. earth has the dark world bosses from 3, fire has the elemental lords from 4, 5 and 6 has some notable bosses from their games in the water and wind dungeons respectively. you will have to run through a couple of dungeons twice to fight them al and to collect the treasure chests, earth is shorter, so you have to make 4 runs through it.
the psp version has another dungeon open up when you are ready to enter the temple of fiends again for the endgame. it has a boss that changes upon how good you are at clearing the floors in it. there are 8 forms of this boss and vary in difficulty.
ff2 has in both the gba and the psp version an unlockable post game story that features 3 characters from the story along with a new 4th one. if you plan on playing this story, make sure to power up minuw, josef, and richard before they leave your party. oyu will be using them in the new story mode.
i haven't checked out the new dungeon but it should have some new weapons for each character that joins you and opens up as you proceed through the story. i plan on checking out when i get ready to play through the psp version soon.
ff4 has a new training dungeon unlocked before the final one and you have the option of swapping characters and getting them exclusive new gear in the new area that opens up at the base of mt ordeals. the post game dungeon has a new boss with an even stronger final weapon for each character and brings back the snes version of zeromus as a super boss. [he had a completely different look in the snes/easy type version]
ff5 adds a new job and dungeon after completing the game. i borrowed the game from a friend before getting to check it out, so my knowledge runs out on this.
@starseeker300 just finished up a full playthrough of the game, so he should be able to fill you in much better on the extra dungeon in 5. and
@Pandaprewmaster325 is very knowledgeable about each game and can help you out with 6. all i know is that a scrapped super boss is brought back for the post game dungeon in that one.
the 3d remakes of 3 and 4 also have some stuff unique to them; if you want me to, i can tell you about those as well.