The historical accounts are anecdotal ("is said to..."), but there are 2 or 3 recent cases according to wikipedia and snopes:
On 24 March 1975, Alex Mitchell, a 50-year-old bricklayer from King's Lynn, England, died laughing while watching the "Kung Fu Kapers" episode of The Goodies, featuring a kilt-clad Scotsman with his bagpipes battling a master of Lancastrian martial art "Ecky Thump", who was armed with a black pudding . After twenty-five minutes of continuous laughter, Mitchell finally slumped on the sofa and died from heart failure. His widow later sent The Goodies a letter thanking them for making Mitchell's final moments of life so pleasant.
In 2003, Damnoen Saen-um, a Thai ice cream salesman, is reported to have died while laughing in his sleep at the age of 52. His wife was unable to wake him, and he stopped breathing after two minutes of continuous laughter. He is believed to have died of either heart failure or asphyxiation
I have found no compelling evidence regarding the historical claims, probably because such accounts are a bit... ridiculous.
There are 2 known accounts of the death of Chrysippus, only one involving laughter.
Diogenes Laërtius gives two different accounts of his death. In the first account, Chrysippus was seized with dizziness having drunk undiluted wine at a feast, and died soon after. In the second account, he was watching a donkey eat some figs and cried out: "Now give the donkey a drink of pure wine to wash down the figs", whereupon he died in a fit of laughter.
King Martin of Arragon apparently died of laughter.
In 1410, when Martin died, apparently of a lethal combination of serious indigestion and uncontrollable laughter, no successor had been properly designated, initiating a crisis of succession.
The death of Urquhart by laughter of is merely a legend according to Wikipedia (unreferenced).
There is a legend that Urquhart died in a fit of laughter on receiving news of the Restoration of Charles II.
However, death and damage from laughter is recognised medically:
We present a case of a 29-year-old previously healthy man who had witnessed a coworker trip and hit his head on the sink at approximately 10 a.m. He subsequently went into a severe fit of uncontrollable laughter that involved leaning forward and crouching down, at which point he began to feel lightheaded and dizzy. He collapsed for 3 seconds with definite loss of consciousness and nonspecific arm twitching.
A 65 year old man developed uncontrollable and unemotional laughter for almost an hour followed by transient right facial-brachial paresis. He had fluctuation of laughter, right facial brachial paresis, and occasional crying.
Gelastic seizures are often associated with hypothalamic hamartomas. However, focal cortical dysplasias can also cause “laughing seizures”, and such cases can be difficult to localize with EEG.
Cataplexy is observed in a subset of patients with narcolepsy and affects approximately 1 in 2,000 persons. Cataplexy is most often triggered by strong emotions such as laughter, which can result in transient, yet debilitating, muscle atonia.
We report the case of a 56-year-old, moderately obese (body mass index of 35) man with a past medical history of sleep apnea, hypertension and hyperlipidemia who suffered from syncope secondary to intense laughter.
Laughter is a complex human behavior that has an emotional and a physical component. We present a patient who suffered syncope as a result of intense laughter, and hypothesize that this is analogous to other types of Valsalva-induced syncope. We emphasize the clinical characteristics that differentiate gelastic syncope from cataplexy.