Eat it.

Fire, and lots of 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.

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.

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.

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.

Recreate that scene from the first triple x where he fly's off the bridge but instead of a car use the mattress

Mail it to the Whitehouse collect.

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!"

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.

Stick it in the front yard with a sign that says

Free soiled mattress!

Whomever takes it is now your bff

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.

Fire cleanses all.

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

Everything is a dildo if you're brave enough.

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

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

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

Put it in a room with my cat for 30 minutes

bonfire time

Use it as a surfboard.

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

Put it out the front of your house with a sign saying 'Free mattress to fuck on, so long as I can film you doing it".

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

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.