Storyboard Body

A character description trope.

Due to The Law of Conservation of Detail, characters rarely have tattoos unless they're in some way important to the character. These don't have to be some extremely significant plot point, but they usually do give us greater insight into the character's personality. The tattoos often involve symbolism of some kind related to the character's past or purpose. Many times the character will be a part of some society, such as a Proud Warrior Race, Gang-Bangers, or The Syndicate.

Sometime this trope is played for laughs.

This trope overlaps with Tattooed Crook. However, in this instance the character is not always a rebel or bad guy.

Examples of Storyboard Body include:

Anime and Manga

Nami has a tattoo that represents her past (as well as her greedy nature). Whether she would have gotten this tattoo if her former "pirate crew" tattoo could have been cleanly destroyed is not quite clear.
- A pirate crew composed of some former slaves took on a tattoo somewhere on their body to hide who had been a former slave and who hadn't to turn the mark of shame into a mark of the bond of shipmates.

Comic Books

Batwoman has several tattoos, including a nautical star and a military symbol. These were given to her when Greg Rucka and J.H. Williams III took over the character, as part of their attempts to make her more than a simple Bruce Wayne clone.
Daken, who's even more of a Sociopathic Hero than his father Wolverine, has a large tribal tattoo on his chest and arms.
Jack Knight as Starman (until his death and regeneration into a new body with no tattoos). Seems to be a defining "Tony Harris is no longer the artist" moment.

Film

Maui from Disney's Moana is covered with animated monochrome tattoos that illustrate significant moments in his life, including a miniature version of himself which seems to act at times as his conscience. They spontaneously appear on his body when something important enough occurs -- as seen at the end of the movie when a tattoo featuring Moana herself appears.
Nikoli in Eastern Promises. Each tattoo has some symbolism. Also a subversion of Tattooed Crook as he is an undercover cop.
The titular character in Soldier. The cheek tattoos are lists of battles and also his rank.
Played for laughs in Blades of Glory as Chazz Michael Michaels' tattoos are for each famous figure skater he allegedly banged.
Lenny in Memento.
Violet in Ultraviolet has tattoos in Thai Hindi on the fingers of one hand, listing romantic life stages. The pinky is "Comrade", the ring finger "Lover", the middle finger reads "Wife". She became a hemophage before the next finger could be tattooed with "Mother".
Enola from Waterworld has a Chinese-looking tattoo on her back. It ends up being the story's MacGuffin.
In The a Team, all four have Ranger tattoos.

Literature

An inversion occurs in The Illustrated Man by Ray Bradbury, as his tattoos tell other people's stories, and eventually how the person watching will die.
A subversion is in Jonathan Strange & Mr Norrell. Vinculus has the complete text of a book of magic tattooed on his entire body. However, this would seem to reveal something about the character.
Played straight in The Godless World Trilogy. The Kyrinin tattoo their faces based on a level system. First for killing an enemy. Second, I currently forget. Third, for stealing an enemy's fire. The Kyrinin achieve the highest level by literally stealing the enemy's cooking fire.
In Stranger in a Strange Land, Patty Paiwonski is entirely covered with scenes from the life of the founder of her religion, Fosterism.

Live-Action TV

D'Argo's tattoos in Farscape mark him as a general. They're actually fake, as he got them so he could act as a decoy to protect his own general.
Jack's tattoos in Lost. The producer chose to openly show actor Matthew Fox's personal tattoos during the first season and eventually reveal the circumstances under which the character got the tattoos with special attention towards their meaning (in traditional Lost-fashion).
Prison Break: It is subverted, though, in that whilst the many tattoos on Michael Schofield's body seem to have some significance to his past or his character, they are actually just there to assist in his breakout from Fox River.
Sam Adama and most of the other members of the Tauron Ha'la'tha on Caprica. The writers even worked the whole thing out.

Tabletop Games

Slayers from Warhammer Fantasy Battle Fantasy Battle are Dwarves who had shamed themselves in some way and seek redemption via death in combat. Part of the Slayer appearance includes ornate tattoos covering most of their faces and bodies.
Werewolves in Werewolf: The Forsaken calculate worth in their society by Renown, split up into five categories—Cunning, Glory, Honor, Purity, and Wisdom. These categories are recognized by the spirits as a form of status, and appear on their bodies as silver brands whenever they enter the Hisil.
Lunars in Exalted have similar silver tattoos, but for different reasons. As Lunars had their Exaltations tainted by the Wyld as a result of hiding out their for centuries, they came up with the tattoos as a way to affix their Caste and protect from the Shaping magics of the Wyld. Part of the process of getting the tattoos involves telling the story of your life and having another Lunar translate it into tattoo form.
Talislantan Thralls, a race of clone troopers so uniform in appearance that they can only be distinguished from one another by their unique tattoos.

Video Games

Played for Squick laughs in The Curse of Monkey Island as you have to remove a tattoo of a map of the tri-island area from a music promoter's back. Played straight in that the whole reason he had the tattoo was that he was traveling to those places all the time.
The Nameless One from Planescape: Torment has a variation of this: He has instructions to find his life's story tattooed on his back.
The Minmatar in EVE Online: The tattoos are supposed to reveal the character's life task or purpose. Also a Rite of Passage.
Psymon Stark of the SSX series. Each of his tattoos are designed by him first, and they all tell a story and carry a deep personal meaning, at least according to DJ Atomika; Of course, you don't get to see many of his tattoos (he's a freaking pro snowboarder, you can't blame him for bundling up), but still.
Runners in Mirror's Edge all have distinct tattoos (including Faith, the player character).
Lilith from Borderlands has a large blue tatoo running across her chest. This tattoo most likely serves as an indicator that she's a Siren, and also draws attention to her, erm, assets. Commandant Steele has a similar tattoo.
In The Bouncer, you learn through text crawls that Koh Leifoh got his tattoos from the government, as part of an attempt to better blend in with the denizens of Dog Street. He pretty much hates them but sees them as a necessary evil to get the mission done.
Jack in Mass Effect 2 has a lot of tattoos. Some are for prisons she's been in, some are for kills (good ones), some are for things she's lost (those aren't your business), and some are there because, well, why not?
- This becomes amusing (relatively, anyway), when you look closely and realise that many of the tattoos on her arms are her different looks in the official Mass Effect concept art.
- She also has a very plausible reason for all the tattoos; the symptoms of the psychological disorder known as Rape Trauma Syndrome often include getting tattoos to reassert control over one's own flesh, and Jack has a ridiculously Dark and Troubled Past.
The bahmi in Rift are stated to cover their skin with Power Tattoos to commemorate their accomplishments. Unfortunately, player characters are somewhat limited in that regard.

Western Animation

Hun, of Teenage Mutant Ninja Turtles (second series) fame, originally started out with two tattoos, depicting the logos of the two syndicates he was loyal to, The Foot and the Purple Dragons. When the character was redesigned for season 7, he no longer sported the Foot tattoo, reflecting how he'd left that particular group behind.
Airbenders have tattoos that map the chi paths in their bodies, and are made to resemble the markings on their Flying Bison. Since as of the current time of the story the Avatar is known to be the last airbender, Aang's tattoos often serve to indicate his identity.

Real Life

Several cultures have tattoos which are significant to their culture and/or tell the story of the bearer. Dwayne Johnson (who is half Wild Samoan) has a fair amount of Culturally Significant Tattoos on his upper body and at least one arm, which are usually digitally removed or covered with makeup for films.