The only thing that could kill Klaus is the White Oak Stake. However, as seen on TVD, on the off chance that someone does successfully take down an Original vampire, the rest of their sire line died too. So killing Klaus would mean the demise of thousands of vampires. Of course, this is only true until Davina breaks Klaus's sire bond in season three of The Originals. His status as a hybrid makes him difficult to execute too. Being the Original hybrid, Klaus could kill any vampire with a single venomous bite. The Werewolf blood running through his veins also made him immune to silver based magic, meaning the Silver White Oak Ash Daggers couldn't be used on him. Lastly, the mere fact that he's over 1000 years old and drank human blood rather than animal blood made him incredibly strong since the level of strength in vampires depends on their age and diet.