The animated series, X-Men: Evolution is based on younger versions of characters from Marvel's long running X-Men comics.
To put some of the more popular characters into a high-school setting, things like the ages of characters and their relationships to each other were changed from the comics.
The comic book character, Nightcrawler is very similar to his counterpart on X-Men: Evolution with some notable differences.
The biggest difference in how Kurt appears in the comics is his feet. His feet are smaller, not as cat-like, and he has 2 toes in the front of each foot and one toe in the back.
In the comics, Nightcrawler is older (somewhere between 25 and 30), and has a larger build. He is a world-class gymnast so he is very lean but quite muscular.
His hair is very curly and he usually wears it rather short compared to Kurt in X-Men: Evolution.
Usually, you cannot see Kurt's pupils at all, so his eyes appear to be solid yellow.
Because Kurt in the comics is older, he has more confidence than in X-Men: Evolution. He is less shy, has grown comfortable with his appearance and does not usually use an image inducer (the comic book version of the "holowatch") unless it is absolutely necessary.
He still acts like a comedian sometimes, but is also highly responsible and has even lead his own team. He enjoys making others laugh, but is also the mature voice of reason in many situations.
Kurt has long had a strong faith in God, and even tried a short career as a Catholic priest.
In the comics, Nightcrawler's teleportation is shown with a large puff of purple smoke and a "BAMF!" noise that has become his trademark.
Usually, he can only teleport a distance of about 3 miles at a time.
There is a limit to how much he can carry with him when he teleports, and there is a great strain in bringing additional people and things with him. In the comics, when people teleport with Nightcrawler, they feel sick and can even pass out. Kurt has sometimes used this to his advantage by repeatedly teleporting an enemy until that person looses consciousness.
In the comics, Kurt always appears to be in shadow even if he is actually under direct sunlight. When it is dark, Kurt blends into shadows and can almost become invisible.
[i]Nightcrawler's Teleporting Dimension[/i]
In the past, the comics have not shown much of the dimension Kurt travels through when he teleports. It occupied by a an old race of demonic-looking mutants that Kurt is decended from. It has a breathable atmosphere, though it smells sulfuric. Time passes differently in this dimension.
The dinosaur-like creatures from the episode "Shadow Dance" have never appeared in the comics.
In the episode Shadowed Past we see that Mystique dropped baby Kurt into a river by accident while fleeing from Magneto. However in the comic, there's no indication that Magneto was involved.
Nightcrawler came to join the X-Men very differently in the comics than in Evolution.
He was raised in a German circus, and grew up to be an acrobat.
Kurt left the circus as an young adult, when it was bought by a man who wanted to put Kurt in the freak show. Kurt came to a small German town where the people believed he was a demon and tried to hunt him down and kill him. They almost staked him through the heart, when Professor Xavier used his telepathy to stop them.
Xavier asked Kurt to join the X-Men and Kurt agreed in a desire to improve himself.
Nightcrawler in the comicbooks shares a close, student/mentor relationship with Xavier much as he does in X-Men: Evolution. However, since Kurt was an adult when they met, Xavier is not as authoritative. Kurt has great gratitude and respect for the Professor and wants to make him proud, but is not as afraid of letting him down.
Nightcrawler and Wolverine both joined the X-Men at the same time as adults, so they do not have a relationship as student and teacher, but as equals. They became beer-drinking buddies and developed a very close friendship and mutual respect for one another. Kurt is one of the only people who can question Logan's actions without making him angry, and pretty much the only one who can make him laugh. Wolverine has even taken orders from Nightcrawler during times when Kurt was acting as team leader.
In the comics, there is a larger age difference between Kurt and Kitty. Kurt was 20 when Kitty joined the team at the age of 13. Much like in the show, Kitty was put off by Kurt's appearance at first, but Kurt was only hurt in a general sense, not because he had a crush on her. Kitty eventually got over her aversion to Kurt's appearance and the two developed an almost brother/sister kind of friendship. Kurt is very protective of Kitty and calls her his "Kätzchen."
[b]Note:[/b] This is for the benefit of people who have seen X-Men: Evolution but are not at all familiar with the comic.