Unclog a Toilet Without Using a Plunger

Here's a quick tip to stash in your mental filing cabinet of home fixes: if you've got a clogged toilet, simply reach for the dish soap.
Once you realize your toilet won't drain, pour half a cup of dish soap into the toilet and let it sit for about thirty minutes. Oftentimes, this is all it needs to unclog on its own as the soap loosens the obstruction and moves it right along.
If after thirty minutes you haven't heard the telltale gurgle of your toilet flushing, heat a large pot of water to just before a simmer on the stove. Do not let it boil, as scalding hot water can crack a porcelain toilet bowl.
By now, your toilet has likely drained at least halfway down. Stand above the bowl and pour the very hot water down the toilet from waist level. It might seem counterintuitive to put more water on top of water when there's a clog, but the Niagara Falls-like force of water rushing down, combined with the heat and soap (which effectively break down matter) work to clear most obstructions from the toilet trap.
Your toilet should automatically drain on its own after this, but very stubborn clogs may need a second or even third douse of hot water.
As a bonus, your bathroom will smell nice and fresh from the soap flushing!