Eat it.

Tie it to the roof of your car, preferably a 25-30 year old subcompact with bald tires and head for the freeway. Make sure to use string, not rope, and don't waste money on too much string.

Enjoy the drive and the problem just goes away.

Light it on fire while it's still in your room. No need to move anything!

Just stack the new mattress on top of the old one. Problem solved.

Take it to the country, find a 10-12" culvert under a driveway or access, pull a winch line through the culvert, attach it firmly to the mattress, winch until the mattress is all the way in the culvert, cut the winch line, and you're done.

Optional: call one of those YouTube drain clearing guys.

Mail it to the Whitehouse collect.

I was at a party once where they burned a mattress, actually it wasn't really a party, just a meth heads house at night time. So you could do that.

Everything is a dildo if you're brave enough.

Fire cleanses all.

Best if done in the living room so your house gets all the smokey goodness.

Poke a hole in it and grease it up. Put it at the end of your driveway with a sign that says "Free Fuckable Mattress, first come, first serve!"

Tear some holes in it, sprinkle in nuts, and leave in your backyard. Congratulations: you now have a rodent hotel!

Hang it on a wall as a statement piece or art with all the suspicious looking yellow stains.

--Edit--

This method has additional merit in that you don't actually even get rid of it.

Attach a rope to it, tie it to the back of some kind of lifted 4x4 or truck, and have a buddy drag it around through the fields while you ride on top of it.

Shred it to bits and smoke it through a bong on public transit

Put it in a room with my cat for 30 minutes

bonfire time

Break into a neighbor's house and put it under their mattress.

Use it as a surfboard.

Throw it in front of your house and leave it there. When asked by your neighbors, say "it showed up there yesterday"

The West Virginia method: take it outside, lean it against your trailer, and forget about it.

Cut a hole in it and fuck it. Keep doing that with new holes until it with falls apart or rots from the inside out.

Donate it to your local indoor climbing wall

Throwing it into the power lines?

Nativity scene, where all of the characters are Barbie’s. Preferably the life sized ones. Dressed in furry costumes. Some of which should be missing limbs, heads, etc. Apply makeup liberally. Use the remaining lipstick to write “a rum pum pum pum” in big bold letters on the front side of the mattress. Place your creation out sometime mid-March for greatest effect.

If you do it just right, they take you to a place where you will get a new mattress, and where the walls are mattresses too!

"donating it"

Fold it length way, rope around each end. Open the middle stick a bit of wood in it......and canoe. Bonus old pillows on a stick for a paddle

infect it with bedbugs, then leave it on the street with a free sign.

Rip off the material, and take the innards to a metal recycling plant near you, for free. (Disclaimer, I'm assuming metal recycling places take things for free in your area)

Eta. Oops. I didn't read. I'll delete.

pack it as tightly as possible, and put it in a stage-box (think musicians, drum set, etc). Go to random hotel check into room with your "instruments" for your "gig" tomorow. switch mattress before leaving next moring.

Stick it in the front yard with a sign that says

Free soiled mattress!

Whomever takes it is now your bff

Put it in the blender piece by piece and flush it down the toilet Or put it in your pocket and feed it to the birds in the local park.

Rip it to shreds, stir fry it and feed it to the homeless.

Fire, and lots of it!