Brumley and Boneh's 2003 paper ("Remote timing attacks are practical") on this is the typical reference: http://crypto.stanford.edu/~dabo/papers/ssl-timing.pdf
You can measure differences of thousands or maybe even hundreds of cycles, but not single cycles. That's below the noise level of a modern computer.
Particularly the section titled "You can’t possibly measure that, can you?"
Any, really, if you hit it with enough copies of each potential input so that you can get enough results to separate the timing difference from the noise. Though the faster, the more samples you can do per unit time, and the closer in network topology, the less sources of variability in latency that make it take more samples you'll have. At least, that's my understanding.
Read Crosby and Wallach's "Opportunities and Limits" paper; the shorthand result of the paper is that across Ethernet you have a window of 100ns, and across an IP network something closer to 30us. The memcmp distinguisher is well below the IP network threshold.