LFSR (linear feedback shift register)
A shift register whose new bit is a linear function of some of the old ones: cheap in hardware, and exactly why it is dangerous as a cipher on its own.
An LFSR is a row of bits plus a feedback function. On every clock pulse the register shifts one step, and the new bit is the XOR of selected taps. With a suitable polynomial the period is maximal, 2^L − 1. That makes it easy to build in hardware and a convenient source of keystream. A5/1, used in GSM, combined three of them.
Linearity is also the weakness. The Berlekamp–Massey algorithm (1968–69) recovers an LFSR of length L from just 2L output bits. Modern designs therefore use LFSRs only alongside non-linear steps, never on their own.