I disagree with some of the information in some of the previous answers. Especially these two:
"We know of a bunch of planets (the gas giants) that are much less dense, but none that are denser."
"A planet with a magnetic field needs an iron-nickel core. "
KELT-1b is estimated to be 4 to 5 times more dense(23.7 g/cm3) than Earth(5.51 g/cm³)
Jupiter has a MASSIVE magnetic field and the most commonly accepted explanation is due to metallic hydrogen, not nickel/iron, in Jupiter's core.
Someone in the comments also mentioned that natural processes could not create denser materials, and another comment mentioned that compaction due to gravity would be reversed once enough mass was removed to reduce the gravity, but I see no evidence to suggest that either of things are true. Fusion in stars can create metals up to the density of Iron, but Earth already has much more dense material than that, created by the earth itself, or on some other planet and later delivered here by collision. I'm fairly certain that gold or Osmium don't dissipate when removed from Earth's gravity well, so there could very well be other materials, even more dense, created in other cosmic planetary bodies, in whole or in part, that would remain stable after being separated from the gravity/pressure where they were originally created.
Having said all that, I can't provide a direct number or calculation for what might be the minimum size (radius/circumference/etc.), though I suspect the calculations in the answer selected by the OP are 'close enough'.
So, here are my two cents on the topic: Assuming some unlikely, though certainly possible (at least within current scientific understanding), occurrences, I would accept the possibility of a planet easily composed of material that would provide a density at least 3 times that of Earth, while at the same time having a small enough radius to give it near-earth-like gravity (plug in those numbers, or anything roughly similar, in to the calculations of the accepted answer, and viola), while maintaining atmosphere and magnetosphere, and other necessities of humanoid life. Then, given the sheer number of galaxies we've discovered, and the sheer number of stars in them, and the sheer number of planets orbiting (and some not orbiting any of) those stars, and the laws of probability, those 'unlikely occurrences' could very well have happened somewhere in our known universe.