FMP! Is based off actual novels that were written (basically big mangas)
A synopsis can be found
Here
Although Ill try to elaborate. Basically a teenage military specialist who works for an underground mercenary organization is given a task. To protect a highschool girl name Kaname Chidori not much is known as to why. but they believe a terrorist organization is after Chidori since she is one of the supposed "whispered." Basically a super intelligent human being who has innate knowledge pertaining to a mysterious "black technology." however this knowledge has remained dormant. So it is up to a mitliary buff souske sagura to try to discretely protect Kaname from any potential threat while attending high school. I dont want to spoil much of the anime for you.
The story hits a bit of everthing action, drama, romance, mechs, and most notably is the humour. Most of the humor is well done one liners and doesnt go over the top. Its short whitty and most of the humour comes from Seargent Souske trying to "act" like a normal teen kid who has been in the military his whole life.
The anime takes place maybe 10-20 years in the future and although their are mechs and high tech weaponry i find it relatively realistic in the sense that maybe in the near future we could have such mobile suits as these. (in other words its not like gundam mechs) they seem more probable and real.
Gonzo animation studio did the animation for the first series and is reknowned for subtly putting 3-D elements into their anime. (other notable animes they also did were Chrno Crusade, Vandread) although FMP! pretty much was their best achievement in terms of art.
There are also two sequels to this anime
Full Metal Panic? Fumoffu which is a series of comedic episodes that take place during the original Full Metal Panic (ive found that some people who hate FMP! like Fumoffu since its so different and vice versa)
There is also Full Metal Panic: The Second Raid which picks up where the first one left off. It is a much darker anime and more adult themed than its predecessor. Its is highly popular and held in higher regard than the original FMP! although only being 13 episodes.
An OVA to the FMP TSR is being made right now. And talks of a FMP the third raid is highly probable due to the previous three series being so popular.
Animes that are similar in Nature: Kinda hard to say, Martian Successor Nadesico or Vandread are the closest i can think of. Its not a mind boggler mecha like NGE or Rahxephon and its not as war driven as the Gundams series.
Basically if you like Mechas you should check it out. Even if you dont i would still at least dl a few episodes and see what you think.
That help?