Lavabit was a web-based email service which kept all email encrypted a key protected by the user's password to how mywallet works. Today lavabit shut down without any advance notice. Details are scarce, but they are claiming that they were being ordered by the us government to do things which they considered wrong. Many believe they were ordered to intercept users (such as Edward Snowden) passwords, or send specific users zero-day exploit code, and chose to shut down rather than comply with the order.
Many other services would and have just simply captured the passwords and gone on with life, many many more are not designed in such a way that they could even resist such an order. The operators of lavabit appear to have taken a remarkably principled position.
Eventually it seems likely to be that hosted wallet services like blockchain.info's my wallet will encounter a similar interaction with the relevant authorities intent on seizing some funds.
It's possible that they could just comply completely, perhaps they could shutdown like lavabit rather than attempt to betray their user's trust, or maybe there is some other possibility.
What would be a best case outcome there?
Edit:And now
silentmail has preemptively shut down rather than be placed in the same position.