In MTG: When a creature is regenerated; are counters removed from it?

No. The Regeneration ability places a Regeneration Shield on the creature. That Regeneration shield says "The next time this creature would be destroyed this turn, prevent that destruction, remove the creature from combat, tap the creature, and remove all damage on it." It says nothing about removing counters, and it prevents the creature from leaving the Battlefield, which also would have removed the counters.