I have gone through the available jobs on Snagajob and this is partial list of the bigger companies that hire 17 year olds along with the job titles in parenthesise of the available positions:
Burger King (Team Member, Shift Coordinator)
AM/PM (Crew Member, Assistant Manager)
Applebee's (Host/Hostess, Line/Prep Cook, Server)
Arby's (Crew Member)
Bed Bath & Beyond (Cashiers)
Bojangles' (Team Member)
Boston Market (Crew Member)
Chic-fil-A (Day Time/Evening Team Member)
Cracker Barrel (Cooks, Servers, Host/Hostess)
Dairy Queen (Cooks, Crew Members, Cake Decorators)
Domino's Pizza (Customer Service Representatives)
Dunkin' Donuts (Crew Members, Shift Leaders)
Golden Corral (Cooks, Line Person, Prep Person)
Hardee's (Crew Members)
Jiffy Lube (Lube Technician)
Kmart (Cashier, Loss Prevention, Replenishment)
Luby's Inc. (Food Attendant, Cashier, Waitstaff)
Marshalls (Merchandise Associate)
Pizza Hut (Team Member, Server)
Sears (Cashier, Sales Associate, & many more)
Sonic Drive-In (Cooks, Carhop/Skater, Drive Through)
Steak n Shake (Servers, Drive Through, Grill, Fountain)
T.J. Maxx (Sales/Merchandise Associate)
Wendy's (Crew Members, Shift Leader)
These are just SOME of the companies that hire 17 year olds and you can find them all and many more on Snagajob. It is free to sign up with Snagajob and in many cases you can apply right there online. At least you can get a great idea of all the different businesses that hire 17 year olds and you can start applying to the ones in your town or city.