Rules of the game:
-Has to be secondary-world fantasy. It's way too easy to find characters in urban fantasy who are lawyers, bouncers, etc., because the modern world's jobs are usually more detailed because familiar to the authors. If it's crossover fantasy, the character's job should actually be important in the fantasy world (instead of their being, say, a secretary on Earth but a mage in the fantasy world).
-No wizards, priests, psychics, soldiers/warriors, thieves, assassins, musicians, kings/queens/princes/princesses, evil henchmen, courtiers, farmers, people whose main occupation is running from the Dark Lord and trying to survive, or apprentices to these people- if that's the main focus of what they do. If the wizard is a wizard on the side but spends most of his time hunting narwhals, this would count. Likewise a gem-cutter who does a little farming.
-It can be a secondary character, but it should be a fairly important one; thus, the quirky monkey-trainer who appears for three pages in Kay's A Song for Arbonne does not count.
-This is NOT necessarily a recommendations list, just a list of odd jobs.
(These are in order by title of book or series).
1632 and sequels by Eric Flint- several jobs, including "doctor, nurse, grower of recreational pharmaceuticals, political agitator, lawyer for the defence in a Church court" (suggested by dorianegray).
Age of Unreason trilogy, by J. Gregory Keyes- philosopher and scientist protagonists (suggested by mad_maudlin).
Alphabet of Thorn, by Patricia McKillip- protagonist is a translator/librarian (suggested by renakazur).
Bartimaeus trilogy, by Jonathan Stroud- Nathaniel is a government official (suggested by kgbooklog).
Beyond the Hanging Wall by Sara Douglass- the main characters are both physicians (suggested by quillblade).
Black Cauldron series, by Lloyd Alexander- Taran is an Assistant Pig-Keeper (borderline case) (suggested by seldear).
Book of the New Sun series, by Gene Wolfe- protagonist at least starts out as an apprentice torturer (suggested by gehayi).
Bridge of Birds, by Brian Hughart- the main character is a scholar, and there's a pawnbroker character (suggested by lnbw.)
Circle series, by Tamora Pierce- metalsmith, gardner, and weaver are three of the four protagonists (suggested by alanahikarichan).
The City, Not Long After by Pat Murphy- street artist characters (suggested by fantasyjax).
City of Bones by Martha Wells- the hero is an archaelogist (suggested by cat_i_th_adage).
The City of Dreaming Books, by Walter Moers- narrator is a writer, and this is central to the plot (suggested by ankewehner).
The Curse of Chalion, by Lois McMaster Bujold- protagonist is a tutor/secretary for a large portion of the book (suggested by kilerkki).
Deadhouse Gates, by Steven Erikson- a character called Duiker is a historian (suggested by theblunderbuss).
Death of the Necromancer, by Martha Wells -protagonist is an actress (suggested by stillsostrange).
Deerskin, by Robin McKinley- the heroine is a princess, but spends most of her time as a kennel girl (suggested by gehayi).
The Discworld series, by Terry Pratchett- the protagonists include Vimes, a city guard, and several secondary characters with the same profession; William de Worde, a journalist; Moist von Lipwig, first a con man and then head of the city's post office; Jeremy Clockson, a clockmaker; and Susan Sto Helit, who works as a governess, a teacher, and an angel of Death (suggested by ankewehner first).
Emerald House Rising, by Peg Kerr- heroine is (aspiring to be) a gem-cutter/gem-worker.
The Etched City, by K. J. Bishop- one major character is a doctor who works on battlefields and at an inner city hospital; an important secondary character is an artist who does peculiar etchings Do you happen to remember what the teacher in A College of Magics taught, just for curiosity's sake? I know there are a lot of teachers of wizardry in some books, mages who have apprentices (suggested by [Bad username: woodburner.]
Ethshar series, by Lawrence Watt-Evans- shopkeeper, innkeeper, and investigator characters (suggested by kgbooklog).
Fevre Dream, by George R. R. Martin -protagonist is a steamboat captain (suggested by gehayi).
Forsala trilogy by Hilari Bell- one of three main characters is a peddler (suggested by wordweaver).
Garrett, P.I., series, by Glen Cook- the protagonist is, entirely unsurprisingly, a P.I., and, moreover, one who solves crimes without being a wizard (suggested by frenchpony.)
Gauche the Cellist, by Kezni Miyazawa- a borderline case, but cellists are not the most common musicians in fantasy, and at least it's not another damn bard (suggested by gehayi).
Ghosts in the Snow and following books, by Tamara Siler Jones- protagonist is both a castellan and a detective (suggested by lnbw).
Glasswrights' Apprentice series, by Mindy Klasky- the heroine, unsurprisingly given the series name, makes stained glass (suggested by kaiz).
The Golden Key, by Melanie Rawn, Kate Elliott, and Jennifer Roberson- main character/villain is a painter/limner (suggested by thornsilver).
The Hallowed Hunt, by Lois McMaster Bujold- one protagonist is a policeman/detective (suggested by kilerkki).
Havenstar, by Glenda Noramly- heroine is a mapmaker, but not officially accepted as such due to gender restrictions (suggested by pling.)
Hawk and Fisher novels by Simon R. Green- Hawk and Fisher are (married) city guards (suggested by fantasyjax).
His Dark Materials, by Philip Pullman- a physicist and former nun is among the protagonists (suggested by gehayi.)
Howl's Moving Castle, by Diana Wynne Jones- Sophie is a hatter and later a servant of sorts (suggested by lnbw.)
Imajica by Clive Barker- forager and whore characters (suggested by fantasyjax).
In the Forests of Serre, by Patricia McKillip- one viewpoint character is a scribe (suggested by zeonn).
The Iron Dragon's Daughter, by Michael Swanwick- protagonist is a factory worker, and later a student (suggested by gehayi).
Kushiel's Dart and following books, by Jacqueline Carey- the heroine is a courtesan/spy who gets off on pain (suggested by taryneve).
Liavek stories by Ford and Bull- actor and shopkeeper characters (suggested by kgbooklog).
The Lions of Al-Rassan, by Guy Gavriel Kay- heroine is a physician (suggested by stillsostrange).
The Liveship Traders trilogy, by Robin Hobb- two characters are sailors and navigators (suggested by gehayi.)
Lord Darcy books by Randall Garrett- protagonist is a criminal investigator, and his assistant a forensic sorcerer (suggested by ahforgetit).
Lord of the Isles, by David Drake- one character is a weaver (suggested by dawnshadow).
Lord of the Rings- Samwise is a gardener (suggested by williamshakers).
Lords of the Sky, by Angus Wells- protagonist is a storyteller (suggested by ankewehner).
The Magic of Recluce, by L. E. Moddesitt- protagonist is both carpenter and Order mage (suggested by yhlee).
Midnight Tides, by Steven Erikson- a character named Tehol is an entrepreneur/con artist aiming to take over the entire economy (suggested by kgbooklog).
Moontide and Magic Rise duology, by Sean Russell- protagonist is a natural historian/philosopher.
Myst: The Book of Ti'Ana, by Rand Miller- Anna is a geologist (suggested by shanra).
The Painter Knight, by Fiona Patton- protagonist is a court painter (suggested by furikudanji).
Perdido Street Station, by China Mieville -protagonist is a scientist.
Pern series, by Anne McCaffrey- Harpers are musicians, but also teachers and spies (probably a borderline case) (suggested by mrs_redboots).
The Philosophical Strangler, by Eric Flint- Ignace is a sort of assassin's middleman, negotiating contracts for the title character (suggested by tumblecoyote).
The Prophecy Machine, by Neal Barrett, Jr.- protagonist is a lizard-maker (?) (suggested by tumblecoyote).
Poison Study, by Maria V. Snyder- the main character is a food taster (suggested by kgbooklog).
Rhiannon's Ride series, by Kate Forsyth- characters are primarily jonglers (suggested by mymonkeysocks).
River God and Warlock by Wilbur Smith- a character who goes through several different professions, including inventor, concubine, and royal adviser (suggsted by kadaria).
The Rope Trick, by Lloyd Alexander- protagonist is a stage magician, no real magic involved (suggested by luhtarian).
Salamander, by Thomas Wharton- protagonist is a bookbinder/printer (suggested by saltnester).
The Sarantine Mosaic, by Guy Gavriel Kay- protagonist/part central focus of the story is a mosaicist. Another is a physician, and several race chariots (thanks to dawnshadow for the reminder).
The Scar, by China Mieville -protagonist is a linguist (suggested by baeraad).
The Secrets of Jin Shei, by Alma Alexander- an alchemist character (suggested by anghara.)
Shadow's Daughter and related books by Shirley Meier- Megan Whitlock, the main character, becomes a merchant (borderline case) (suggested by othercat).
Shadows Linger by Glen Cook- Shed, part-narrator of the story, is an innkeeper and graverobber (suggested by thelittlebudgie).
Solomon's Ring, by L. Sprague de Camp- an accountant protagonist (suggested by dsgood).
Staying Power and other stories, by Anne Sommerville- a botanist character, a physician/researcher, and an animal breeder (suggested by logophilios).
Stealing the Elf-King's Roses, by Diane Duane- the heroine is a forensic investigator who also prosecutes cases (suggested by kgbooklog).
Steerswoman books, by Rosemary Kirstein- heroine is a wandering scholar (borderline case, as the books are close to not being fantasy) (suggested by kgbooklog).
Threshold by Sara Douglass- POV character, and several others, are glassworkers, and one is a priest who worships a mathematical god (suggested by quillblade).
Thursday Next series, by Jasper Fforde- protagonist is a detective, of sorts (suggested by ankewehner).
Tinker, by Wen Spencer- protagonist is a junkyard owner (suggested by fadethecat).
Tooth and Claw by Jo Walton- one character, a dragon, works in the city planning department (suggested by lccorp2).
Twelve Treasures series, by Rosemary Edghill- fairyland librarians (suggested by kgbooklog).
Vincalis the Agitator by Holly Lisle- the main character is a playwright (suggested by thestephy).
The Vlad Taltos sequence by Steven Brust- Cawti, a main character, becomes a revolutionary after holding another job first (borderline case) (suggested by othercat).
Voyage of the Shadowmoon, by Sean McMullen- a bellydancer character (suggested by zeonn).
Warslayer, by Rosemary Edghill- heroine is an actress (suggested by kgbooklog).
The Water Mirror by Kai Meyer- protagonists are apprentices to a mirror-maker and a weaver, and do not have magical powers (suggested by anima_mecanique).
Westmark series, by Lloyd Alexander- a printer's apprentice, a dressmaker, and a laundress (suggested by mhari).
When the King Comes Home, by Caroline Stevermer- heroine is a painter (suggested by kgbooklog).
Wind on Fire trilogy, by William Nicholson- a librarian and an emperor who becomes a cowherd (suggested by parametric).
Wiz Biz, by Rick Cook- protagonist is a computer programmer who finds a way into a fantasy world (suggested by rickgriffin).
Worldweaver trilogy (forthcoming), by Alma Alexander- the protagonist's father is a feral library tamer (suggested by anghara).
I know I've read more- they just aren't coming to me right now. Anyone got more?