To retain a vital anagram in different languages, the full name of Tom M. Riddle has been changed in most non-English versions, sometimes even quite drastically. In German, for instance, his name is Tom Vorlost Riddle (surprisingly close to the original, considering the vastly different language), in Swedish it's Tom Gus Mervolo Dolder, and in Icelandic it's Trevor Delgome(!), which sacrifice the "riddle" wordplay altogether. (Source: DVD translations and subtitles)
In Disney Channel's showing, the scene where Colin Creevey introduces himself to Harry by taking his picture is extended by Colin explaining his family history.
German theatrical version was cut (the Willow tree bashes the car three times less, Ron being attacked by a spider in the car, close up of a bone in the dungeons, Harry being pursued by the Basilisk, Harry uses the tooth only once to kill Voldemort, the death of Voldemort, the death of the Basilisk) to secure a "Not under 6" rating. Additionally some dialogue was changed (when Harry hears the Basilisk at the beginning, it says "I will get you" instead of "I will kill you"). This version was released on DVD & VHS in Germany and Austria but not in Switzerland where the uncut version was released (resulting in high exports to the two other countries). The uncut version of the movie was rated "Not under 12" and was shown on TV and released on Blu-ray.
On the DVD's "deleted scenes" section we have a scene that shows Lucius Malfoy and son coming to Burgins & Burke to sell magical items of 'questionable' nature, which introduces Lucius to the story (and perhaps more importantly, how he treats his son when _not_ in a crowd) earlier than in the theatrical version. As with the other deleted scenes on the DVD, this one was also inserted at its proper place within the film in the Disney Channel showing.
Some of the dubbed versions change the names of a few characters, to match their translated novel counterparts in each respective language. One good example is Hermione, who in the German version (of all the Potter films/books) is named Hermine.
The 2009 Ultimate Edition DVD/Blu-ray release features an extended cut of the film running approx. 174 minutes (vs. the theatrical's 161 minutes). It edits back in most of the scenes included as deleted scenes on the previous DVD release.
In Disney Channel's showing, there's a scene in the library after Justin had been petrified, which has been extended. Instead of Harry just overhearing some whispers, he hears a whole conversation between three students debating whether he is the Heir of Slytherin.
In Disney Channel's showing, during the Dueling Club scene, Justin Finch-Fletchley introduces himself to Harry and tells him that he's a Muggle-born.
In Disney Channel's showing, there's one scene with Harry, Ron, and Hermione in the hospital wing after her Polyjuice Potion incident but before her release thereof.
In Disney Channel's showing, after the camera pans away from the students applauding Hagrid's return in the Great Hall, the scene which was at the very end of the credits in the theatrical version is shown. In a shot of the front of a wizarding bookstore, a book called "Who Am I?" by Professor Gilderoy Lockhart is on display. The author's picture on the cover is of Lockhart struggling confusedly in a straitjacket, and humming the movie's theme music.
In Disney Channel's showing, there is a scene where Crabbe and Goyle, just awakening from the mickeyed muffins, run into Harry and Ron as they're running from the Slytherin dorms. Harry and Ron are halfway through transforming back into themselves, and actually look like two completely unknown students.