Cache timing attacks are a class of side-channel attacks that is applicable against certain software implementations. They have generated significant interest when demonstrated against the Advanced Encryption Standard (AES), but have more recently also been applied against other cryptographic primitives. In this paper, we give a cache timing cryptanalysis of stream ciphers using word-based linear feedback shift registers (LFSRs), such as Snow, Sober, Turing, or Sosemanuk. Fast implementations of such ciphers use tables that can be the target for a cache timing attack. Assuming that a small number of noise-free cache timing measurements are possible, we describe a general framework showing how the LFSR state for any such cipher can be recovered using very little computational effort. For the ciphers mentioned above, we show how this knowledge can be turned into efficient cache-timing attacks against the full ciphers.