Kathy is right, something like the Big Shot/Big Kick is the best. Any of the steel-ruled, thick metal dies can cut through felt easily. This would include the Accucut and Ellison lines as well, which are much more expensive and usually in schools, libraries and scrapbook shops.
You might also be interested in the Accucut Go! Fabric die cutting. It's just like a regular die cutting machine, but they are targeting quilters - and you might find their range of dies appealing.
http://www.accuquilt.com/