I hear a lot of prizes are things like the rare number lamps that sell for 9,000 Bells at regular stores. My sister actually got a throne from Wishy too! I don't know the full list of things possible to get, but the items are probably all pretty rare and expensive.
^ Yes, sometimes there are meteor showers, when shooting stars flash across the sky. If you press A when one flashes by, your character will bow and you'll get a letter from Wishy the Star, with a present attached (usually a spotlight item).
In New Leaf so far, I've gotten a dolly and a tower of pisa. In Wild World I got a throne once and I'm hoping to get one in NL this way too eventually ^_^
Meteor showers will be on the bulliten board the day of the shower. After 7pm go outside. Have nothing in your hands. Press up on the D-pad and stand still (I like having my character looking away/north). When a shooting star goes across the screen, press the A button. If done correctly, the character will turn and face you/south, put their hands together and the shooting star will get larger/brighter. You can do this several times a night, but you will only get one gift in the mail the next day from Wishy. The gifts are always spotlight items. I've gotten several Rococo items, numbered lamps and sci-fi items. Good Luck.