The Combinatorial Object Server (CoS) can generate perms/combs, sets/multisets, partitions, DeBuijn seqs/Lyndon words/necklaces, graphs, and a few others, all through a web interface. Unfortunately, it only typically works well for queries that have relatively few results. (It will truncate the responses to 1000 objects)

http://combos.org

(Edit: referring back to your original specific request, it can also produce all polyominoes of fixed size or all polyomino covering of a user-specified shape, and several others, and output as either text or images)