We've replaced the Inbox with a general, un-named stream that lives on your user page (which used to just show Your Streams). This "general stream" is like your Inbox with the big difference that you can publish cards in it.
We noticed a lot of people were having to create a named stream just for this (with names like "Random Thoughts"). Now you don't have to. If you have such a stream and you'd like the cards moved over to your general stream, just email firstname.lastname@example.org and we can move them over for you.
You can read more about some of the motivation and details of the general stream feature in the General Stream stream.