Different characters and the things they swear on:

Harry Potter: Firebolt, most probably. Swear on your Firebolt!

Ron Weasley: Food. Swear on roasted ham and Yorkshire pudding.

Hermione Granger: Test grades, books etc. "Hey, I don't think it's good to swear by the way!"

Ginny Weasley: uh... Bat Bogey hex, I suppose?

Draco Malfoy: Swear on your super awesome good looks.

Dolores Umbridge: Swear on teacups and pink cardigans.

Rita Skeeter: Swear on Quick Quotes Quill.

Remus Lupin: Swear on beloved Thomas Hardy, Charles Dickens and chocolate of course.

James Potter: Swear on Quidditch and the immeasurable live for Lily Evans.

Peter Pettigrew: Swear on the whole sticks if Honeydukes and Hogwarts Kitchens.

Sirius Black: "No, if I have to swear on something, I'd definitely swear on my own undeniably awesome self."
_quoted by the infamous Sirius Orion Black himself.

Fred and George: Swear on the Weasley Wizard Wheezes merchandise.

Luna Lovegood: Swear on the horn of a Crumple Horned Snorcack.

Lord Voldemort: Swear on everlasting life and eternal power over all.

Mad Eye Moody: "Constant Vigilance, didn't I tell you? Constant Vigilance!"

Bellatrix Lestrange: Swear on the Dark Lord.

Nymphadora Tonks: "Well, anything would do for me. Just don't call me Nymphadora!"

And I know these aren't all of the characters, they're just a few of them that came up in my head.