TheBooBooKitty suggested I move this from Charcter Guide to Ducktales. TheBooBooKitty was right.
Many of the characters on DuckTales were originally created by Carl Barks for the Uncle $crooge series of comic books. They are marked with an asterisk in the list below. The others were created especially for this cartoon series. Note, though, that these character descriptions refer to the characters in the cartoon, not the originals in the comic books.
* "Uncle" Scrooge McDuck. Scrooge was born in Scotland, where he earned his first dime (an American dime, interestingly) shining shoes. He keeps this dime under a glass dome in the library of his mansion, although he's been known to use a decoy from time to time. He earned his fortune by "working smarter ... not harder." As a shoeshine boy, he created a mechanical contraption that could shine multiple shoes simultaneously. This earned him enough money for passage to America, where he travelled to the Klondike, where he aquired a claim and mined the gold there. It was in the Klondike that he met Glittering Goldie, who would both win and break his heart. With the money he earned from his gold mine, he established a financial empire and became the Richest Duck in the World. He keeps a significant portion of his fortune in cash, held in a gigantic money bin, which makes a tempting target.
Scrooge is, above all, cunning and devious. He makes his living being "tougher than the toughies and smarter than the smarties." He is a ruthless businessduck and he has earned every penny. He can identify every coin in his money bin and how he earned it. He has a love of adventure; he relishes the chance to go out and explore some ancient ruins or investigate a far-off occurrence. But underneath his rough exterior is, unsuprisingly, a heart of gold. He cares deeply for his family and personal employees, and would do anything to protect them.
Huey, Dewey, and Louie. (Note: They appeared in many, many $crooge comics, but were not created for that series.) These triplets are Scrooge's grandnephews, through one of his sisters and her daughter (Donald's sister). They came to live with Scrooge, over his objections, at his mansion when Donald joined the Navy. It wasn't long, though, before their resourcefulness proved immensely valuable, and, since they are family, Scrooge soon accepted them fully.
The three are distinguishable by the colors they wear: Huey in red, Dewey in blue, and Louie in green. They sometimes trade in their baseball caps for brown furry ones with tails, as they are members of the Junior Woodchucks. Their Junior Woodchuck manual contains useful survival information that they and Scrooge put to good use.
Webigail Vanderquack. Webby is Mrs. Beakley's granddaughter who lives with her at the McDuck mansion. She is rarely without her rag doll, who is dressed in the same shade of pink as Webby is. She seems to be about five years old and, as such, is more often a liability than an asset when she tags along on an adventure. Her biggest motivation is to not be excluded by the Nephews, which she often is, because she's half their age and a girl.
Mrs. Beakley. You'd think with Scrooge's fortune, he could hire more than two domestic servants. As it is, though, Mrs. Beakley is half of his staff. She serves as maid and cook, as well as the Nephews' governess. Rotund and grey-haired, she rarely came into play unless her granddaughter Webby was involved or if the Nephews had to outsmart her to get out of the mansion.
Duckworth. The other half of Scrooge's staff, he serves as his butler, chauffeur, and occassionally groundskeeper. Like the Beagle Boys and the Duckburg police force, Duckworth is a dog. He has an English accent and is rarely anything but completely proper and loyal to his employer.
Launchpad McQuack. Scrooge's personal pilot, Launchpad is among the best when it comes to flying. When it comes to landing, however, he takes personal pride in being the worst. He keeps a painstaking record of every crash. Launchpad has so much practice at crashing that the only casualty is usually the aircraft. He comes from a successful family of stunt pilots, who still love him despite his inability to land. Launchpad later went on to become Darkwing Duck's sidekick.
Bubba Duck. While travelling through time into the past, Scrooge, the Nephews, and Launchpad encountered this young prehistoric duck and his pet dinosaur Tootsie. They inadvertantly brought the two back to the present and were forced to take them in. Bubba has very limited language capabilities but he is much stronger and tougher than the Nephews. Huey, Dewey, and Louie, who were about the same age as Bubba, tried to include him (moreso than they did Webby, certainly), but his lack of understanding caused many problems.
Fenton Crackshell. Hired on as Scrooge's accountant, Fenton had a keen mind for numbers. He was previously a bean counter (literally), where he displayed an uncanny ability to count beans almost instantaneously. His new job helps him support his mother, who sits in her trailer and watches soap operas in her bathrobe.
Unfortunately, Fenton lacks confidence -- he has none. His social ineptness is a hindrance to his attempts to start a relationship with the beautiful Gandra Dee. This changes when he puts on the Gizmoduck suit, which he stumbled into purely by accident (Gyro set the command word to be 'blatherskite,' which coincidentally was part of Fenton's favorite exclamation, "Blabberin' Blatherskite!"). As Gizmoduck, Fenton is charismatic and confident, a stark contrast to his normal personality, which helps maintain the secret.
* Gyro Gearloose. Gyro is a typical eccentric inventor -- mind-staggeringly brilliant but socially incompetent. He has a assistant in the form of a six-inch semi-intelligent robot with a lightbulb for a head. Gyro's greatest accomplishment is the creation of the Gizmoduck suit, into which he placed every useful feature he could think of. He created it at Scrooge's request to protect the Money Bin; Scrooge was going to hire someone appropriate to fill the suit but decided to keep Fenton on in the role after he stumbled into it.
* Flintheart Glomgold. The Second Richest Duck in the World. Although he was South African in the comics, Flinty is Scottish like Scrooge in the TV series. This is probably because he wears a tam-o'-shanter and a kilt. Glomgold is always, always, always, trying to become the Richest Duck in the World, but Scrooge is always, somehow, one step ahead. There is little that Glomgold won't do to reach his goal, even going so far as to hire the Beagle Boys on occasion.
* Magica de Spell. This black-haired Slavic-accented witch is perhaps Scrooge's most dangerous foe. She is a powerful magic-wielder, but she is often reckless with her power. She, too, has hired the Beagle Boys to help her out, but they often suffer the results of her magic more than Scrooge does. Magica's obsession is with obtaining Scrooge's Number One Dime, which she insists is extraordinarily lucky and the key to all of his wealth. Scrooge adamantly disagrees, but still refuses to give it up -- just in case! Magica's familiar is a talking raven, who happens to also be her brother; he helps out in hopes she might change him back one day.
* The Beagle Boys. Not to be confused with Beagle Bros. These ne'er-do-well perpetually-incarcerated canines are Scrooge's most frequent adversaries. Unlike in the comics, individual Beagle Boys in the cartoon have distinct names and personalities. There are a plethora of Beagle Boys, led by the criminal genius Ma Beagle, including Big Time Beagle, Burger Beagle, Baggy Beagle, Bouncer Beagle, and Baby Face Beagle. Their only purpose in life is to break into Scrooge's Money Bin and obtain all of his cash. They never ever try to get his assets any other way -- always directly through the most impregnable building in Duckburg. They have come tantalizingly close at times, but always end up back in the slammer by the time Scrooge is done with them.
Donald Duck. Donald appeared frequently in the comics on which many episodes of DuckTales were based, but only rarely in the cartoon, since he'd joined the Navy. He did show up from time to time, however, where we saw him being abused by his commanding officer.
Doofus. A fellow Junior Woodchuck, Doofus often appeared with the Nephews and Launchpad (in his role as their Head Woodchuck). Launchpad took a distinct liking to the nerdy, rotund little fellow, unlike many of his peers.
Mrs. Featherby. Scrooge's long-suffering secretary, Mrs. Featherby had the unpleasant tasks of attempting to keep unwanted visitors out and informing her employer of all manner of bad news.
I used the Encyclopedia of Walt Disney's Animated Characters by John Grant for spellings and some minor details, but this is mostly from memory.