Update: Some games are available for gifting.
It is currently possible to gift: World of Warcraft, WoW mounts/pets, StarCraft 1/2, Warcraft 3+expansion, Diablo 2+expansion and Virtual tickets for Blizzcon.
From the blizzard support page:
Warlords of Draenor, Diablo 3: Reaper of Souls, and Heroes of the Storm are currently unavailable to gift.
To gift an eligible item to a friend, click Gift instead of Buy Now on
the item’s page. During check out you can enter your friend’s email
address. We’ll send a key code to their email address, and you’ll
receive a purchase receipt at your registered Battle.net email
If you entered the wrong email address, you can find the key code for
your purchase on the Order History page. You can copy this code and
send it to your friend.
Your friend must have a Battle.net account to claim a game key. If you
gift them a World of Warcraft pet, mount, item, or game time, they
must have a World of Warcraft licence in good standing (not banned or
suspended) attached to their Battle.net account.