How big can a "rocky planet" get?

Is there a theoretical limit to how big an earth-like planet (or one like Mercury, Venus, or Mars) can get? (I seem to remember that several earthy exo-planets were at least a bit bigger than our ball of rock, dirt, and water.)

It depends. What do you call a “rocky planet?” Jupiter has a “rocky planet” of multiple Earth masses as its core. So in a natural mix of elements in a protoplanetary disc, after a number (that I don’t know off the top of my head) of Earth masses of rocks and iron build up, enough volatile elements are retained to make it into an ice/gas giant. If you don’t want to call Jupiter a really gassy rocky planet, then the limit would be whatever that “keeping all the hydrogen” margin is.

If you want unnatural conditions–say an advanced species is collecting all of the refractive elements that they can find and gather them into a lump, then I’d call the limit around 1.4 solar masses, at which point it would become a neutron “star” (if you can call it that without it ever haven been a normal star.)