The list of commonly used stream ciphers is very short because there's really only one. RC4, developed by Ron Rivest, is essentially the only stream cipher that has been widely deployed. RC4 is very fast and found in wireless networking devices, as part of Wired Equivalent Privacy (WEP) and WiFi Protected Access (WPA), among other places. WEP does not offer much protection because a wireless network with lots of WEP traffic will reuse portions of the key stream if you listen patiently for a while. This is exactly what you weren't supposed to do with stream ciphers. This is more a poor use of RC4 rather than a flaw in the algorithm itself. WPA is a replacement for WEP that provides better security.
The RC4 key stream is generated from a 256 byte state array using a pseudorandom number generator. Each time random bits are generated, the state array gets slightly scrambled so that future output bears very little resemblance to past output. The state array is initialized by the encryption key. Encryption keys can be between 1 and 256 bytes long, with shorter keys essentially repeated to pad out the length. Initially, the state array has a fixed value. The algorithm is then initialized by looping over the repeated encryption key and scrambling the state array according to the key bit values. The encrypted stream is generated by taking the exclusive-or of the bits of the input stream with the randomly-generated bits.
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