Do thin clients leak which addresses you own? According to this, thin clients use bloom filters to request "addresses and transactions they are interested in to the peer".  And according to this, bloom filters are used to help prevent the SPV peer from "know[ing] which transactions belong to the client and which don't.".

But the accuracy of bloom filters, and thus how easily the peer can deduct which addresses belong to the client, is determined by the thin client.

So how well do the major thin clients (Electrum, Multibit, Mycelium, etc.) protect the privacy of the addresses belonging to your wallet from their SPV peer?
Electrum: 

No protection, the server you are connected to knows every address you own and will own in the future. If you use Tor your IP address is hidden, but the addresses are still associated. Bloom filters are not in use for this client.

MultiBit

In theory the bloom filter can be modified to include junk data to hide your addresses with loads of fake ones, currently this is disabled for speed and so there's no protection. Your peers know your IP address and the contents of your wallet, Tor is not supported.

Mycelium

I believe this client uses BitcoinJ (same as MultiBit) so the same caveats apply.