Mickey Mouse's girlfriend, Minnie, made her film debut in "Steamboat Willie" on November 18, 1928. Named after the artist that did her vocals, she was a high-pitched and jolly character. The first voice of Minnie Mouse was Marcellite Garner, from the Ink and Paint Department at the Disney Studio. In the studio, Ms. Garner was known affectionately as "Minnie", a joke on how she refused to relinquish power to taller people because of her stature (about 4'9"). She was succeeded by several others from that department, and currently the voice is supplied by Russi Taylor, as of 2002.

Minnie Mouse has had more appearances in public than she has on screen. She did not have her own cartoon series, but appeared in 73 cartoons with Mickey Mouse, Pluto, Donald Duck, Pete, and just about every other major Disney character. She has been a popular character at the Disney theme parks, and 1986 was declared Minnie's year, giving her much-deserved time in the spotlight. For that year, Mickey was seen only on 3 occasions. Since the theme park opened in 1955, Minnie has appeared in costumes puppeted by over 700 names and voices. Minnie Mouse has two nieces, Melody and Millicent, who appeared in a few comic book stories, but never on screen. Some of Minnie's favorite sayings include: "Why, hello!" "Aren't you sweet!" "Yoo-hoo!" and the affectionate "Oh, Mickey ..."
Photo Clip: http://adisney.go.com/vault/archives/characterstandard/images/minnie_portrait.jpg

Some of Minnie Mouse's film appearances:

Building A Building: Minnie's singing ability and a relationship with Mickey blossom in the Oscar®-nominated film "Building a Building". Mickey is a steam shovel operator on a construction job who buys a box lunch from Minnie, a roach coach owner's daughter. Pete, one of Mickey's enemies, attempts to run away with her but Mickey is in hot pursuit throughout the building. When a girder (large metal beam) falls on Pete, Mickey and Minnie escape on her lunch wagon into a happy sunset. The film was Minnie's second appearance, and introduced her to Pete, Bill, and Papa, her father. Papa only had one scene, but has been added to Minnie's legend by association.
Photo Clip: http://adisney.go.com/vault/archives/characterstandard/images/a04c3b.jpe

Mickey's Rival: This film introduces Mickey's first romantic rival, Mortimer. Interestingly, Mortimer was the name for Mickey that Walt originally planned, but his wife talked him out of it. Mortimer invites Minnie out on a date, and tries to hit on her. As he reads Minnie cheap pickup lines, he harasses Mickey to no end. But when a bull is set loose, it is Mickey who is the one to rescue Minnie. At this point, Minnie begins to notice that Mickey also loves her, and that Mortimer is not the man for her. However, the film ends before she does anything about this. This is Minnie's first film where she had the most lines of any character.
Photo Clip: http://adisney.go.com/vault/archives/characterstandard/images/a04d3b.jpe

The Nifty Nineties: Minnie initiates romance with Mickey for the first time in "The Nifty Nineties" (1890's, that is). Turn-of-the-century Mickey and Minnie attend a vaudeville show and later ride in a new "horsecar" that ends in a wreck when a cow interferes. Mickey saves Minnie in daring heroic style, and steals away Minnie's heart. There are currently 2 reels of "The Nifty Nineties" remaining in the world, owned by the New York Museum of the Moving Image, and the Disney Archives. Each reel has an estimated value of 1.2 million USD. This is also Disney's first movie in Technicolor! The only reason for the excessive use of vibrant and odd colors is to play with this technique, and test its limits.
Photo Clip: http://adisney.go.com/vault/archives/characterstandard/images/a04e3c.jpe as well as /a04e3b.jpe

And Minnie's latest movie:

Runaway Brain!: Dr. Frankenollie, a mad scientist, transplants Mickey's brain into a monster's body and vice versa. The monsterized Mickey, known as Julius, becomes obsessed with pursuing Minnie, and Mickey, whose intentions are misunderstood because he is in the monster's body, tries to save her. The name of Dr. Frankenollie was inspired by the famed animators Frank Thomas and Ollie Johnston. As the usual Disney childens' movie style, the plot is quite predictable, yet very cute in its portrayal. This was Russi Taylor's first full-length production playing the voice of Minnie Mouse.

As of December 15, 1966 (the day Walt Disney died), Mickey and Minnie were still dating. I can find no definitive proof that they ever married. (I thought I had proof, but Roninspoon has killed that idea, and I cant manage to find hard sources.)

Sources:
The Disney Archives (http://disney.go.com/vault/archives/characters_ai.html)- Some of Minnie's history paraphrased. Portions of the movie summaries were either lifted or paraphrased.
My grandfather, Irvin, who worked for Disney as an animator for a long time.
Gollier, Brent. The History Of The Cartoon. McGraw Hill Publishing, New York. 287 pages, (c)1989.
Biography of Walt Disney (http://disney.go.com/vault/read/walt/index.html
This was an entry for Everything Quests: Hollywood's Golden Age.