While never announced by Sony, educated speculation concluded the PS4's eight-core Jaguar processor runs at a clock speed of 1.6GHz. A recent post by Sony UK on Google+ has given that guess a thumbs-up, comparing the latest-gen console's power to that of a PS2. Sorry, make that 43 PS2s.
As you can see in the image above, which can be found on Sony UK's Google+ page, the PS4 is apparently equivalent in performance to 43 PS2s, though the formula Sony's used to come up with the number doesn't provide a clear picture. Basically, it's multiplied 1600 by 8, and divided it by ~299 (the rough speed of the PS2's CPU in MHz).
The problem with this calculation is it doesn't take into consideration the efficiency of the pipelines, cache performance, branch prediction and all the other bits and pieces that make up a CPU's architecture. Outside of the same product line, raw cycle comparisons have been fairly useless for years.
It'd also be more appropriate if the PS3 was used instead, but that's much less favourable — the PS3 used the custom-engineered Cell processor, which had a PowerPC core and eight "Synergistic Processing Elements", or SPEs, running at 3.2GHz. Even taking away the two SPEs in the PS3 that aren't available for use by developers, the PS4 is a little over half as powerful as a PS3, according to Sony's maths.
Then there are the GPUs, but I think there's enough headache material here without diving into that kettle of fish.
Sony UK [Google+]