Bullgatortail hits the nail on the head when naming the differences here, but I would like to expand upon the one that I thought was the most glaring when first reading the book and watching the movie (and then using the movie to teach the book for many years):  the neglect of the character of Soda.  Let us look at the character of Soda (full nickname of "Sodapop") in the book and then conclude with what we know of him in the film.

As Ponyboy's big brother, one would think Sodapop Curtis would have received a bigger billing in the film.  Soda is almost seventeen and has dropped out of high school.  Regardless, he is the guardian of the Curtis family and always attempts to make peace.  He is also the most gorgeous of the Curtis brothers.  Sodapop got his nickname because of how happy and cheerful he always is.  He has no need for liquor because he gets drunk on life, especially anything having to do with horses or rodeos.  Sodapop is also a very understanding character who always listens.  Of course, he is also prone to teasing (especially Darry).  Soda is devastated when his girlfriend Sandy, heads to Florida.

In conclusion, the sad mention of Soda is absolutely pitiful.  All we know is that he is certainly one of the greasers and that there is one mention of his relationship with Sandy.  Everything else is left out.  It is a perfect example of how a director and/or screenwriter must choose which characters to focus upon in a movie.

bullgator's answer is very good, but there's always more to say about how a written work such as The Outsiders has been adapted into film. I would encourage you to think about how there is more to the differences between the novel and the film than matters of differences in the storyline or the appearance of the characters. These differences are nearly infinite.

In the opening of the novel, for example, we are delivered information directly through the narrator, Ponyboy, and have no idea at this point that Ponyboy is actually writing all of this information down as a sort of make-up assignment for an English class. The film, by contrast, opens with Ponyboy writing his composition. The framing device (writing the paper for the English class) is presented at the beginning and end of the film, whereas the novel presents it just at the end.

The first spoken words of the film are identical to the first sentence in the novel, presented in a voiceover. From there, we as shown rather than told a great deal of the opening sequence: in the film, we are shown Ponyboy observing himself in a mirror outside the movie theater (in the book, he tells us what he looks like and what he wishes he looked like); in the film, we are shown the tension between the Greasers and the Socs when Ponyboy is chased down and tormented (again, in the book, we are told this information in a sory of general summary); etc.

Novels and films are very different creatures. It would be an impossible task to list all of the differences between the two, but it's a great fun to learn a little about filming techniques and to begin to appreciate just how a compelling novel such as The Outsiders can be transformed into an equally compelling film.

The Francis Ford Coppola production of The Outsiders is actually more faithful to the original novel than most film adaptations. Probably the most glaring difference was the decision to cast Matt Dillon and his black hair as Dallas Winston, who had blonde hair in the novel. Other differences:

• The dream sequence in the movie actually shows the Curtis brothers' parents being killed in a car/train crash. In the novel, it was only mentioned as an auto accident.
• Dally is shown robbing the store and being wounded in the film; in the novel, he tells that he has robbed the store via telephone, and he is not wounded.
• An early scene in the movie shows Dally chasing kids who are playing cards; this is not mentioned in the novel.
• The rich west side Socs and poor east side greasers are changed to rich south and poor north in the film.
• Of all the characters, Soda seems to be less developed in the film. There is only one mention of his relationship with Sandy, and we hear nothing of Soda's love of horses or rodeo.