Gmail – How to Restore Inbox View

Gmail labels are different than folders, in that a message (or conversation) can have multiple labels. Generally speaking a message can only exist in one "folder".

It's easy to simulate labels as folders, however. Just make sure a message only ever has one label. "Inbox" is a special label in Gmail, but it's still just a label.

To do this automatically, when you create your filter to move the message to the label(s) you want, also check "Skip the Inbox". Then new messages that meet your filter criteria will not be in the Inbox.

As of November 2012 this is now possible with a simple search

has:nouserlabels

Finds all messages without any of your own labels (excludes automatic labels like inbox, spam, and trash). Since Gmail applies labels to individual messages, you might see results that appear to have labels; in this case, another message in the same conversation thread has had a label applied to it.

Source: Search for emails by size and more in Gmail - Official Gmail Blog

Source: Using advanced search - Gmail help