Can you gift games to yourself?

Yes!

Games you buy as a gift can be stored in your gift inventory. From there, you get the choice to either gift them to someone via e-mail or to a Steam friend, or add them to your library.

Simply choose the "Add to my game library ..." option instead of "Send gift ..." in your Steam inventory.

As of 4th of May, 2017, this is not possible anymore. You can either purchase the game for yourself, adding it directly to your library, or send it to a friend, who can either accept it, adding it to their library, or refund the game, refunding your money.

Here is the official blog post explaining the change.