From the original run: basically any scene in which J.R. has a clever/charmingly nasty quip which rips into Pam or Ray. The best example of this is in the episode "Ewing Inferno" at the end of Season 6, during a scene between Pam and J.R. at the Ewing Oil offices.
Also from the original run:
Episode 54, where JR gets shot. The mother of all Cliffhangers and the second-most watched TV episode of all time, second only to M*A*S*H's finale.
Episode 93, where JR gets up the gumption to rebuild his life and the Ewing empire after Jock's death. Actually, pretty much any scene with JR and Jock's portrait qualifies.
Miss Ellie has a few: in Episode 14, she chases off a nosy reporter after her sons are thought to be dead after a plane crash; Episode 88 sees her berate Jock's friends for taking advantage of his absence; Episode 102 sees her have a fantastic scene where she comes to grip with Jock's death.
Episode 217. Angelica Nero and a poisoned hatpin. Nuff said.
Episode 222. Pam wakes up to find a a guy who looks like Bobby in her shower. Your mileage may vary about this one.
Episode 251. "John Ross, THIS is Ewing Oil.", as JR indicates Jock's portrait.
Episode 277. JR's attempt to take over Weststar is thwarted by a whole bunch of enemies, but the coup de grace is delivered by the most unlikely person: his wife Sue Ellen...
...who in Episode 281 shoots JR after he tosses her lover Nick over a balcony.
Episode 291 had two with old nemesis Jeremy Wendell getting trapped by the Ewings and sent to jail; and then a fantastic entrance by Cally Ewing as JR's new wife.
A meta-example for the new series: the fact that the old cast has been integrated with the new characters in a way that doesn't seem out of place or forced is really awesome. Let's face it, it wouldn't be Dallas without Bobby and JR.
Christopher and John Ross burying the hatchet in "Family Business" and going into business together. It even motivates JR to stop being an asshole for just a minute and sign the deed to Southfork back over to Bobby. Unfortunately, it only lasts for one episode before everything goes to hell...
The wordlessly-coordinated asskicking the Ewings lay on the Venezuelans in "Blame Game," capped off by Drew saving Christopher and Elena from Vicente by shooting Vicente with his rifle.
After hearing one too many insults about J.R. at his wake, it's Christopher, not John Ross, who throws the first punch at a heckler. The two then quickly dominate the wake and soundly beat the hecklers and troublemakers.