A third season of K-ON! has been indirectly announced by way of DVD pre-orders for the title opening.
Amazon (and other retailers) have begun listing future K-ON! DVDs far in advance:
けいおん!!(第2期) 9 (Blu-ray 初回限定生産) [Blu-ray]
K-ON!! (Season 2) 9
This obviously suggests at least 18 episodes (unless it came with only one episode per disc, which at $70 per disc would hopefully be unlikely), and a second season of K-ON!! (with two exclamation marks), both pointing to a continuous run of two 12-episode seasons, for a possible total of 24.