The Disney Renaissance

As previously mentioned, the Disney Renaissance was from the years 1989-1999.
During this time period some of the greatest Disney animated films were made. 
These films were made during the Disney Renaissance:

The Little Mermaid  (1989)
Beauty and the Beast (1991)
Aladdin (1992)
The Lion King (1994)
Pocahontas (1995)
The Hunchback of Notre Dame (1996)
Hercules (1997)
Mulan (1998)
Tarzan (1999)
Fantasia 2000 (1999)

(Note that two other films, The Rescurers Down Under and Oliver and Company, were also made during this time period, but they are not usually considered part of the Renaissance)

The Little Mermaid:

This was the film that dragged Disney out of the "dark ages" of the 80s.  The combination of characters, animation, and music created a film that harkened back to the Disney classics.  The film won two academy awards, one for Best Score and one for Best Song (Under the Sea).
Trivia:
This was the first fairy tale Disney made into a animated film since Sleeping Beauty (1959)
During one of the first scenes, when King Triton is arriving at the musical, Mickey, Donald, and Goofy can be seen in the crowd.
According to Disney, Ursula is actually Ariel's aunt.
Ursula is not an octopus.  She has six arms, not eight.  This was done becasue six arms are easier and cheaper to animate than eight.

Beauty and the Beast:
Considered by some to be the greatest animated film of all time, this remains the only 2D animated film to be nominated for Best Picture.  It won the award for Best Score and received three nominations for Best Song eventually winning for the title song.
Trivia:
The famous ballroom scene from the film was Disney's first large scale use of computer generated animation.  Although it had been used before, it had never been used on as large a scale as this.
In early concepts for the film there was a song called "Human Again" in the middle of the film.  It was sung by the enchanted objects and was about their longing to be human again.  It was cut from the original film but was put back in for a special DVD release ten years later.
when Gaston falls from the tower at the end of the battle scene small skulls appear in his eyes.  Although nearly impossible to see normally, if you pause the film at that moment you can see them.

Aladdin:
Continuing Disney's legacy, Aladdin also won Academy Awards for Best Score and Best Song for A Whole New World. 
Trivia:
In the original release there was  line in the opening song that said "where they cut off your ear if they don't like your face"  This was highly criticized for being racist and in later releases the line was replaced.
Each of the characters in Aladdin are essentially a single geometric shape.

The Lion King:
One of the most Disney popular films, this film once again continued Disney's winning streak of winning Best Score and Best Song (Can you Feel the Love Tonight).
Trivia:
Disney actually brought the animals  they were going to animate to the studio for life-action reference.  They had also done this during production of Bambi.
During Hercules, Hercules is seen wearing Scar's skin while posing for a portrait.  This is a reference to both the film and the Nemean lion of Greek Mythology.
At the climax of "Toy Story" the song Hakuna Matata can be heard playing on Andy's radio.

Pocahontas:
I bet you saw this coming, this film also won Best Score and Best Song (Colors of the Wind)
Trivia:
In the original concepts, Pocahontas had three animal friends.  Meeko the raccoon, Flit the hummingbird and a turkey.  The turkey was eventually deleted from the film.

The Hunchback of Notre Dame:
One of the darker Disney films, this one was not quite a popular as the previous ones.  However it still boasts excellent animation and story.
Trivia:
Two of the gargoyles are named after the original book's author.  Victor and Hugo.
This adaption of the original book is drastically different than the source material.  In the book, the hunchback is not always the "good" guy and Quasimodo, Phoebus, and Esmeralda all end up dying.

Hercules:
There really isn't particulary interesting trivia that I could find this movie other than the previously mentioned Lion King one.

Mulan:
Trivia:
This film is based on an old Chinese story.  In China this story is as well known as the story of Cinderella is in western countries.
One thing this film takes advantage of color. The color of the backgrounds change constantly to reflect the charcters mood or the story.  One example is that when Chang almost kills Mulan the sky gradually gets redder.  When he throws away the sword the sky returns to deep blue.

Tarzan:

Trivia
This was the first animated film to make use of a new technology called "Deep Canvas".  This allowed the animators to "paint" on the three demensional backgrouds, resulting in more realistic effects.

Fantasia 2000:
The last film of the Disney Renaissance.  It seems appropriate that the last film should be a new take on an old classic.
Trivia:
Originally this film was to have more sequences from the original Fantasia.  These included the "Dance of the Hours" "The Nutcracker Suite" and "The Sorcerers Apprentice"  However, due to time constraints only the Sorcerers Apprentice appeared in the final film. 
For years had tried to make a short film from Hans Christian Anderson's "The Steadfast Tin Soldier."
Eventually it was added to Fantasia 200 and combined with "Piano Concerto No. 2" by Dimitri Shostakovich.
After a few years a second Fantasia sequel was planned, but was quickly shut down. 
The short film "The Little Match Girl" also based on an Anderson fairy tale, was planned to be in this, but was released as a stand alone short film.