The ZeroAccess botnet is one of the largest known botnets in existence today with a population upwards of 1.9 million computers, on any given day, as observed by Symantec in August 2013. A key feature of the ZeroAccess botnet is its use of a peer-to-peer (P2P) command-and-control (C&C) communications architecture, which gives the botnet a high degree of availability and redundancy. Since no central C&C server exists, you cannot simply disable a set of attacker servers to neuter the botnet. Whenever a computer becomes infected with ZeroAccess, it first reaches out to a number of its peers to exchange details about other peers in its known P2P network. This way, bots become aware of other peers and can propagate instructions and files throughout the network quickly and efficiently. In the ZeroAccess botnet, there is constant communication between peers. Each peer continuously connects with other peers to exchange peer lists and check for updated files, making it highly resistant to any take-down attempts.
Update - October 03, 2013:
For a more detailed look into ZeroAccess and Symantec's sinkholing of roughly half of the entire botnet, read the Security Response whitepaper:
ZeroAccess Indepth