Balled up paper is a fave in our house.
Apparently so are used tissues.... I have no idea why but they keep stealing them out of the bins.
Socks, they're stealling socks.
Our Smoke has a clothes fetish and will steal, lay or otherwise make it difficult to get dressed.
Cat tunnel, tent, boxes, mice, hedgies (stuffed hedghogs, we have 5 spare because they destroy them after a while), few fishing rod type things or things on a stick (which are also good for unblocking sinks as my husband discovered).
Pretty much whatever they get their paws on