The following is a list of occupations possible in the Harry Potter universe. If you do not find an occupation on this list, it does not mean your character cannot have it. It is just a list of suggestions for occupations in the Wizarding World.
I've seen this list used in a few games and can't honestly tell you who originated it. So credit doesn't go to me and I will gladly credit if anyone knows who the originator is.
JOBS FOR THE BEST AND THE BRIGHTEST
Auror (Dept. of Magical Law Enforcement)
Unspeakable (Dept. of Mysteries - Ministry)
Hit Wizard, Magical Enforcement Squad (Ministry)
Curse-Breaker (Gringotts or Private)
Healer (St. Mungos or Other)
Obliviator (Dept. of Magical Catastrophes)
Accidental Magic Reversal Squad (Dept. of Magical Catastrophes)
Invisibility Task Force (Dept. of Magical Catastrophes)
Employee in International Magical Office of Law (Part of Dept. of International Magical Cooperation)
Employee for Wizarding Examinations Authority
Editor for Daily Prophet
JOBS FOR THE SOCIAL
Food Service/Cook (Possible places: Hogwarts Express, Madam Puddifoot's, Florean Fortescue's, Three Broomsticks, various pubs/tea houses/bars/restaurants/cafes in Diagon Alley and Hogsmeade)
Waiter/Waitress (The Hog's Head, The Leaky, Madam Puddifoot's, Three Broomsticks etc)
Travel Agent at Terrortours
Nanny/Childcare
Muggle-Worthy Excuse Committee (Dept. of Magical Catastrophes)
Employee in Cauldron Shop in Diagon Alley
Employee at Flourish & Blotts
Employee at Gambol & Japes
Employee at the junk shop in Diagon Alley
Employee at Quality Quidditch Supplies in Diagon Alley
Employee at Scribbulus Everchanging Inks in Diagon Alley
Employee at second hand robe shop in Diagon Alley
Employee at Dervish & Banges
Employee at Honeydukes Sweetshop
Employee at Madame Puddifoot's
Employee at Scrivenshaft's Quill Shop
Employee at Zonko's Joke Shop
Musician
DJ or personality on the Wizarding Wireless Network (WWN)
Reporter (Daily Prophet, Witch Weekly, The Quibbler)
Journalist/Editor (Daily Prophet, Witch Weekly, The Quibbler)
Photographer (Daily Prophet, Witch Weekly, The Quibbler)
Employee at Weasley's Wizard Wheezes
JOBS FOR THE POLITICAL/LAW-MINDED
Employee in office of International Confederation of Wizards, British Seats (Dept. of International Magical Cooperation)
Employee in International Magical Office of Law (Dept. of International Magical Cooperation)
Employee at International Magical Trading Standards Body (Dept. of International Magical Cooperation)
Employee in Improper Use of Magic Office (Dept. of Magical Law Enforcement)
Employee for the Wizengamot (Examples: Secretary, Wizengamot Assistant, Personal Assistant to a Member of the Wizengamot, Chief of Staff for member of the Wizengamot)
Employee for Committee On Experimental Charms
Employee at the Society for Tolerance of Vampires
JOBS FOR THOSE WHO LIKE HELPING PEOPLE
Healer (St. Mungos, Private Practise, Etc)
Mediwizard
Professor at Hogwarts
Nanny/Childcare
Obliviator (Dept. of Magical Catastrophes)
Accidental Magic Reversal Squad (Dept. of Magical Catastrophes)
Employee in Misuse of Muggle Artifacts Office
JOBS FOR THOSE WHO LIKE WORKING WITH MAGICAL CREATURES
Dragon feeder at Gringotts
Dragon Keeper (Romania, Scotland, etc)
Executioner of dangerous animals (Ministry)
Training Security Trolls
Employee in Dept. for the Regulation and Control of Magical Creatures
Employee at Eeylops Owl Emporium
Employee at Magical Menagerie in Diagon Alley
Employee at the Post Office
Employee at the Society for Tolerance of Vampires
Employee at Goblin Liaison Office
Employee at a Magical Zoo
Magizooligist
Studier of Magical Creatures in their Natural Habitats