I have Varolz, the Scar-Striped out along with a few minor creatures. My opponent on his turn casts Supreme Verdict. Before the Verdict resolves can I use Varolz's regenerate ability by sacrificing one of my lesser creatures? Will my Troll survive the Verdict?
Sure you can.
With Supreme Verdict on the stack, you respond by activating Varolz's regenerate ability. This resolves.
Supreme Verdict now resolves, destroying all creatures. Varolz's regeneration shield protects him, and he becomes tapped and survives the Verdict.
Obligatory comp rules citation:
614.8. Regeneration is a destruction-replacement effect. The word "instead" doesn't appear on the card but is implicit in the definition of regeneration. "Regenerate [permanent]" means "The next time [permanent] would be destroyed this turn, instead remove all damage marked on it and tap it. If it's an attacking or blocking creature, remove it from combat." Abilities that trigger from damage being dealt still trigger even if the permanent regenerates. See rule 701.12.
This is all pretty basic stuff of course. Perhaps some confusion arises from the fact that Supreme Verdict "can't be countered". This just means that it counterspells etc won't work on it, not that there is no possible means of escaping the Verdict's destructive effect.