Satoshi Dice requires wallets to be able to receive coins from the same address they are sent.
What are some notable examples that are compatible and incompatible with this?
What are the technical reasons behind such an incompatibility?
BitLotto has the same restrictions and maintains a list of compatible wallets. Currently that list includes:
Essentially everything else is a hosted (shared) EWallet and therefore is not compatible. This includes EWallets at exchanges, EWallet sites like Instawallet, and other services like mixers and more.
Satoshi dice uses the same address bitcoins were sent to send them back. There no wallet that does not permit that, how could you spend coins if at first you cannot receive them. The kind of "wallet" satoshi dice is refering to is like you try to spend bitocoin from a broker service (like Mt.Gox) the address they use is not assured to be yours (and the coin will not return back to you)