The Legend of Zelda: A Link to the Past/Riddle Quest

The Riddle Quest is an entirely optional sidequest that will give you a new sword technique as well as some memorabilia.

Prerequisites
You need to have won 10 medals in the Four Swords for collecting the most Rupees, otherwise you can't play. You also need the Bug-Catching Net (see the main walkthrough for how to get it).

Once you meet the requirements head to the lumberjacks' house just west of Death Mountain. Go inside and talk to Q. Bumpkin, and agree to answer his riddles. He gives you a Basket, which replaces the "?" in the item screen. Once he's told you what to look for you can go hunting for it.

For each riddle simply use the Bug-Catching Net to bag the creature or item the clue refers to and confirm you want to capture it. You can replace it by simply catching something else, but unlike Bottles you can't let the creature out again yourself. The Basket becomes a permanent part of your inventory, but once all of the riddles are solved you can't use it again.

The Clues
Once you have brought him the Cukeman, Q. Bumpkin will teach you his family's secret sword technique. Simply charge your sword until you hear the sound, then wait to hear it again. When you hear it a second time press rapidly and move in the direction you want to go. This special move depletes your Magic Meter.

The Carvings
If you sprinkle Magic Powder on a carving it will begin to sparkle. Sprinkle again and the carving becomes colored. Sprinkle a final time to switch the carving to an alternate form. The cucco swaps with one of the sickly Dark World birds, Princess Zelda swaps with an old lady, and Link swaps with his bunny form. The Link carving wears whatever tunic you currently have. You can also throw the carvings around if you wish. Whatever changes you make to the carvings or their location will be reset when you leave your house.