Most commonly, in U.S. collections, you will find gutter pairs in the 1935 Special Printings.
A gutter pair, as the name implies, is created when a stamp from one pane and a stamp from another pane have a wide gutter between them.
Here's some examples from the 1935 Special Printing:


These are your standard pairs with the gutter between. To obtain these you needed a full sheet of panes, which were available to collectors in 1935 when these stamps were released. Another popular configuration is a cross-gutter block of four. Here's an example:

To give you a better idea of the configuration possibilities, take a look at this next item. It is a single pane of the souvenir sheet surrounded by parts of eight other panes. You end up with four cross-gutter blocks and several gutter pairs.

There are perforated gutter pairs, as well. These are generally the result of a problem in the production of the stamps, such as a foldover, and are usually an EFO as a result. In the modern era, there are die cut gutter pairs created from press sheets as well.
Hope this helps.