This is the biggest secret in Super Mario World. It is called the “Top Secret Area". I completely missed this the first three times I played Super Mario World. Then out of boredom the fourth time playing Super Mario World I discovered it.
It is very simple to find. First go to Donut Plains #1 and get a cape from one of the Caped Koopas. Then go to Donut Ghost House #1. At the very start of the stage fly up to find a ledge. Follow this to be rewarded with several 1-ups. Then finish the stage and it will open a level called “Top Secret". It isn't actually a level but just a screen like Yoshi's House.
Every time you enter this level you will be rewarded with your choice of two capes or two flowers and a green Yoshi. This makes the game much easier as it is accessible before the second castle. Since it is so unknown for first time players and even veteran players it is very easily missed. It seems too easy to find to be such a unknown secret.
Another reason people often miss this secret is because they look at the World Map and think the Ghost House can't branch off to another path other then straight to the castle or into the lake. The other reason is because you can't get a cape in the levels previous to the Donut Ghost House #1 besides Donut Plains #1 which is two levels before it.
You follow the directions above and pat yourself on the back for finding the Top Secret Area in Super Mario World.
Matthew Corgan is the author of http://www.originalnintendo.net and http://nintendowee.blogspot.com
You can play Duck Hunt online also at http://playduckhunt.blogspot.com