Apple has just updated iTunes to allow users to gift paid apps to other users in the same country (i.e. US App Store to US App Store -- no cross-border gifting!). The feature appears as part of the drop-down widget in iTunes on the desktop.
Similar to the previous music-gifting feature, once you've opted to gift a paid app you're taken through several screens where you're asked to enter your name, the email address for the person you're gifting (for smooth service, make sure you use the email associated with their iTunes account), a personal message, and confirmation.
Note: iTunes rolled out new terms and conditions to presage the new functionality, so you'll have to agree to those before you can use it.
We've tested it out and it seems to work well. Let us know if you get in the giving spirit (or if you receive any gifted apps).
More screenshots after the break!