By definition, all Atari 2600/VCS emulators are cycle accurate.
That machine required very precise timing of the CPU to drive the video output.
There are a number of other cycle-accurate emulators, including some you woudln't expect, like a cycle-accurate emulator for the C64 floppy disk (needed for anti-piracy and some high-end demos that use the floppy like a co-processor).
For the uninitiated, the Commodore 1541 (and later 1570) are external floppy drives that contain their own 6502 CPU and work RAM. In fact, you could daisy-chain two of them with a C64, tell one to copy a whole disk from the other, and disconnect the C64; the drives would continue to work as they do not rely on the C64 at all.
The "C64" demo "Freespin" wires the drive's data cable directly into the monitor's data cable to play a demo (including audio!) without an actual C64 involved at all:
That machine required very precise timing of the CPU to drive the video output.
There are a number of other cycle-accurate emulators, including some you woudln't expect, like a cycle-accurate emulator for the C64 floppy disk (needed for anti-piracy and some high-end demos that use the floppy like a co-processor).