The Enterprises:

USS Enterprise NCC-1701-E
Soveriegn Class

Mission #1: To patrol the Romulan Neutral Zone while the Borg invade Fed. space.
Mission #2: Stop Dominion raids.
Mission #3: To rescue a malfunctioning Data. Commanded by Cpt. Jean Luc Picard.
Refits: One
Last Seen: Exiting the Briar Patch after saving the Ba'ku planet from the Son'a.
Weaponry: This ship is the finest out there with Quantum Torpedos, ablative armor, and a bunch of powerful phaser arrays. Optimized to fight the Borg.

USS Enterprise NCC-1701-A
Constution Class

Mission #1: To rescue hostages from planet Nimbus III.
Mission #2: Escort Klingon Chancellor safely into Federation space.Commanded by Captain James T Kirk
Refits: None
Last Seen: Badly damaged by a Klingon Bird of Brey that could fire while cloaked. Was decomisined.
Weaponry: This ship was a modifies version of the orginal Constitution class ship. It's weapons were also modified.

USS Enterprise NCC-
1701-B
Excelsior Class

Mission: To rescue El'Laurian ships trapped in an unknown energy wave. Commanded by Captain John Harrimen.
Refits: None
Last Seen: Rescuing one of the three ships in the energy wave and taking heavy damage. Unknown past that point.
Weaponry: This ships weapons were never seen, however it looked to be very formiddable as all Excelsior Class ships were at the time.

USS Enterprise NCC-1701-D
Galaxy Class

Mission: To explore the Galaxy and seek out new life. As the flagship of the Federation, the ship took on many important diplomatic and combat roles as well. Commanded by Captain Jean Luc Picard.
Refits: One refit.
Last Seen: Crashed on planet Viridian 3 thanks to the Klingons
Weaponry: This ships weapons were state of the ark when it was first launched. It holds up against any foe admiraldly, even a Borg Cube.

USS Enterprise NCC-
1701-C
Ambassador Class

Mission: To rescue The Klingon outpost at Nirenda III. Commanded by Captain Rachel Garrett.
Refits: None
Last Seen: Destroyed at the hands of 4 Romulan Warbirds. Stoped a war with the Klingons by dying tring to save them. A temporal rift was involved.
Weaponry: This ships weapons were obviously good enough to hold off 4 Romulan Warbirds for quite some time...

USS Enterprise NCC-1701
Constitution Class
Mission: To Explore the galaxy and discover new life forms. Make allies and warn the Federation council of any threats.
Commanded by Captain James T. Kirk
Refits: Had one refit.
Last Seen: Self-Destructed by Kirk and crew.to prevent the Klingon from capturing it.
Weaponry: This class of ship had standard weapons of the time which included Photon Torpedos and Phaser Banks. They were powerful for that time period.

Other Federation Ship Classes:

The Centaur Class: This class was used for battle support in the Dominion War. It had powerful phaser arrays and a fray of photon torpedo launchers. Captain Charle Reynolds commanded one of these ships in the effort to win the war.

The Oberth Class: This class was used only for scientific purposes, nothing else. It had basically no weaponry at all.

The Soyuz Class: This ship was only seen once (that I know of). It was an enhanced version of the Miranda class. Captain Morgan Bateson commanded one of these.

The Miranda Class: This ship was built sort of as a light cruiser. It had good weapons including photon torpedos and the shot shot type phasers. This ship is mainly used for scientific purposes, although it may be used in battle.

The Constellation Class: This ship was supposed to be built for speed. At the time it launched, it's four warp nacelles were supposed to give it an advantage, though it didn't. Picard commanded one.

The Akira Class: This ship was built for the Dominion War. It was and performed great on the front lines. It had modified torpedos and phasers alond with powerful shielding and ablative armor.

The Nebula Class: This was purely scientific when it was built. Though it had it's share of weapons, the extra triangle shape saucer section made for specialty in certain studies. Once the Dominion War started, these were even being used to fight with.

The Prometheus Class: There is only one ship in existance of this class: The USS Promethus. It was an experimental ship using the new multi-vector assault mode and a lot of new guns

The Steamrunner Class: This ship was mainly used for support in the Borg invasion of 2373. It is cheap and contains all the necessary tools to put up a good fight. It can also be used for other things as well.

Structures:

The Olympic Class: This ship was actually only in the future. In a world Q created for Picard, this was a Medical Ship commanded by Cpt. Beverly Picard.

The Intrepid Class: This ship is mainly used for Diplomatic occasions and scientific research. The USS Voyager was built  by this class. That ship got lost in the Delta Quadrant, and after 4 years is still doing fine. The ship has quantum and photon torpedos and a powerful main phaser array.

Deep Space Nine Station

The Defiant Class: This ship was an experimental one. Constuction started on it when the Federation first learned of the Borg threat. When the Borg finally attcked again, the Defiant class wasn't finished yet, and afterwards was put aside and construction stopped, until the Dominion came around. Then it was finished and the USS Defiant emerged.

A station that played a key part in the Dominion War. Was built by the Cardassions and was originally called Terok Nor. It is now used to protect the planet Bajor, and to guard the Bajoran Wormhole. All races use the staion.