For those of you just getting into the Harry Potter series of books like I am, you'll notice that the first book has a LOT of characters. I, at times, found it hard to remember who was who in the first few chapters. To help, I've made a list of the characters that present themselves in the first book.
Harry Potter - he is of course the namesake for the series of books and very quickly begins to play the role of a hero. To me he seemed a bit uncomfortable in his own skin which is no surprise since he was not only orphaned as a baby, but also taken in by his aunt and uncle who locked him in a cupboard underneath the stairs of their home. Harry does not find out about his "magic" past (and future) until he is approached by Hogwarts, his new school.
Petunia Dursley - Petunia is Harry's aunt and sister to Harry's late mother. Although her sister was able to perform magic, Petunia has no abilities of her own (a non-magical person is called a Muggle). She is against magic and makes every effort to keep Harry in the dark about it. She caters to her son, Dudley, but treats Harry as a burden to her.
Vernon Dursley - Petunia's husband and Harry's uncle. He is very much the head of the household and also does not believe in magic. He is rather mean to Harry, and also keeps Harry from finding out the truth about his parents and his past.
Dudley Dursley - Harry's cousin and son of Petunia and Vernon. Dudley is a spoiled bully and knows how to get his way with his parents. He is privileged, and likes to rub this in Harry's face.
Fred and George Weasley - a set of trouble-making twins that attend school with Harry. Their younger brother, Ron, is in Harry's class
Ron Weasley - Ron is Harry's best friend at Hogwarts. He comes from a poor family and has several siblings. Everyone in his family is magic, so he often lives in the shadows of his other family members.
Hermione Granger - When she is first introduced in the book, Harry and Ron both find her bossy and annoying. She is a know-it-all, but has a lot of skill as far as magic is concerned. She excels at school, and tries her best to fit in even though she has a fear of failure. By about mid-novel she has become a friend to Harry and Ron.
Draco Malfoy - An arrogant bully who is in the same year as Harry at Hogwarts. He makes it clear that he does not like Harry, and does not respect anyone who does not have the same financial or magical background as he does.
Neville Longbottom - a nerdy child in the same year as Harry at Hogwarts. He is always forgetting things, and is not as skilled as the rest of his class. He is somewhat of a friend to Harry, although it is not clear if Harry and his friends really consider Neville their friend, or only feel sorry for him.
Professor Dumbledore - Headmaster of Hogwarts. He is a great wizard with a bit of a sense of humour. He seems to be taking Harry under his wing and guiding him to becoming a great wizard as well. He is a bit of a mystery, but I am sure we will learn more about him as the stories progress.
Professor McGonagall - She is Transfiguration teacher at Hogwarts, which makes sense since she often disguises herself as a cat. She is also head of Gryffindor House (Harry's dormitory at Hogwarts).
Professor Quirrell - He is the "Defence Against the Dark Arts" teacher at Hogwarts. He wears a turban that conceals a surprise towards the end of the first novel. He seems very nervous and jumpy, and has a bit of a stutter.
Professor Snape - Is teacher of Potions at Hogwarts and also head of Slytherin House (Malfoy's dormitory). He is quite mean to people he does not like, and makes a point of being especially humiliating towards Harry. Harry considers Snape an enemy early in the novel.
Hagrid - Hagrid is the gamekeeper at Hogwarts. He is a giant and hairy man, and was first introduced to us when he went to retrieve Harry (in order to take him to Hogwarts). He once attended Hogwarts, but was expelled, and that is why he is now only the gamekeeper. Dumbledore seems to really trust Hagrid, and Harry immediately considers Hagrid one of his closest friends. Best description of Hagrid so far in my mind would be that he is a "gentle giant" who does not mean anyone any harm.
Filtch - He is the school's caretaker, and loves to catch students where they are not supposed to be. He tours the halls at night, and seems to get a thrill from the hunt. Harry and his friends have a couple of close calls with Filtch.
Mrs. Norris - Filtch's pet cat who helps him find students who are sneaking around the school.
Professor Sprout - Herbology teacher
Professor Flitwick - Charms teacher
Professor Binns - History of Magic teacher. He also does not realize he has died and has become a ghost.
Madam Hooch - Quidditch coach (a sport Harry and Malfoy participate in - on broomsticks).
Peeves - a poltergeist who appears out of nowhere and causes trouble for anyone who encounters him.