Dealing with a clogged toilet is a gross job, but we all have to do it eventually. This isn't guaranteed to work every time, but I think you'll agree, it's worth a try.
Add a liberal amount of dish soap to the toilet. Since the dish soap is heavier than the water, it will sink straight to the bottom.
Wait for about 20 to 30 minutes. The dish soap will seep into the clog, lubricate the toilet's trapway, and loosen up the clog.
Pour a bucket or pitcher of hot water directly into the bowl. The soap will slowly work it's way through the trapway, then free your clog.
Flush your toilet to refill your bowl.