Well, something simple to do is - Exchange Brown Bag Lunch Day.
Everyone brings in a brown bag lunch, puts it on a table, then selects a different brown bag to eat.
Everyone makes one lunch that way and everyone gets a surprise.
If you want, no one needs to identify who made what.
Another thing we use to do, especially around the holidays was - The Great Cookie Exchange.
Everyone brings in a large batch of a of home made cookie and an empty box.
When everyone has all their cookies on the table, everyone goes around and takes a few of each kind till their empty box is filled.
You go in with one type of cookie and can come out with a dozen or more different types. It's a great way to try all kinds of cookies and everyone only made one type (or variations of similar types).