We know that LFSR are used in the design of stream ciphers. Block ciphers with modes of operation such as counter are also used in the design of stream ciphers. What other things are available to design stream ciphers ?
There are stream ciphers based on non-linear feedback shift registers and one can also use a (cryptographic) hash-function to generate the key stream in a way comparable to block-ciphers in OFB-mode etc. Something very close to this is the cipher Salsa20/12, but I would rather view it as a distinct design. Furthermore stream ciphers can be constructed based on a sponge-structure as is used for SHA-3.
Have a look at the eSTREAM-portfolio to get an overview of different constructions: http://www.ecrypt.eu.org/stream/
Just look at Cryptographically Secure Pseudo random bit generator which are based on integer factorization, discrete log problems. They do not use any LFSRs.
SEAL developped in 1993 by IBM (Don Coppersmith) and RC4 (1987 - Ron Rivest)) from RSA Security are very known streamciphers which are not based on LFSRs.