According to the Washington Post, White House Chief of Staff Rahm Emanual's office is replete with iPad users:

Emanuel just got his, as did senior adviser David Axelrod and deputy press secretary Bill Burton. Both communications director Dan Pfeiffer and press wrangler Ben Finkenbinder have one on order. Economic adviser Larry Summers takes his to staff meetings.

They seem to have a penchant for financial and newspaper apps and the public domain iBooks at the moment, though Burton admits to Scrabble and the last season of Lost.

The legislative branch, not unexpectedly, is split over the iPad.

[Washington Post]