Angela leaves for Europe with her father (who will be stationed there) for one year. She and Shawn decided to not say goodbye and instead say "I love you."
Jack is cut off from his rich step-fathers money and decides to join the peace corps with Rachel after graduation.
Topanga gets a summer internship with the law firm Brown/Elliot (in NYC) and they give her a scholarship to NYU Law School so she can eventually go to work for their firm. Cory initially does not want to go, but realizes it's for the best and helps Topanga feel better about going. Eric decides to move to New York with Cory and Topanga, and Topanga decides Shawn should come with them also.
Alan & Amy stayed at their home where they still had Morgan and Joshua to continue raising.
Mr. Feeny continued to teach at the college (though a future episode showed him retiring in 2006).
In the final moments, before the original four (Cory, Shawn, Topanga & Eric) depart for New York, they find Mr. Feeny in their old elementary/middle school classroom. They ask him if there was anything left for him to teach them, he replies by telling them his work with them is done and they are ready for the world. He then says "Believe in yourselves, dream, try, do good." to which Topanga replies, Don't you mean, 'do well'? and Feeney then asserts, No, I mean, 'do good'. Eric then asks Mr. Feeny to tell him and the others that he loves them, but Mr. Feeny says that "there is a line between teacher and student that must never be crossed." Mr. Feeny does not tell them he loves them, but they all say their sad and heart-felt goodbyes to him. When Mr. Feeny tells Cory that he will remain there, Cory tells him that he will always be with them, as long as they live. After the four leave the classroom, Mr. Feeny says "I love you all... class dismissed" and leaves the room.
Partially because the actors (and presumably, off-camera, the crew) were so emotional and partially because show creator/director-of-the-final-episode Michael Jacobs wanted to capture all the real emotions of the actors, the final scene was done in one take.