I'm pretty sure there's a Wikipedia category for this, so I'll just mention a few obscure/cool ones from around the 19th century.
Albert Kamehameha - only child of Kamehameha IV of Hawaii. He died at the age of 4 and was the only child of his generation in the entire royal family. Another chiefly family was elected to the throne in the 1870s, leading eventually to the American takeover.
Alfred, Hereditary Prince of Saxe-Coburg-Gotha - only son of Prince Alfred, Duke of Edinburgh. He killed himself during his parents' silver wedding anniversary over some personal crisis involving syphilis.
George, Crown Prince of Serbia - he didn't die before his parents, but he was barred from the throne after an incident in which he kicked a servant to death. He was locked up in a lunatic asylum during his younger brother's reign but allowed to live normally under Tito. His reign might have been quite interesting (in the Chinese proverbial sense) what with 2 World Wars, the rise of Communism, etc.
Prince Ferdinand Philippe, Duc d'Orleans - eldest son of Louis Philippe of France, he fell out of a carriage and banged his head, dying in the process. He was one of the two or three popular members of his family, so public opinion took a turn for the worse, especially as the new heir to the throne was a small child. This may have exacerbated the Revolution on 1848.
Agustin Jeronimo de Iturbide - eldest son of Emperor Agustin of Mexico. His father spent less than a year as Emperor, but that kind of thing leaves an impression on a teenager, so AJ spent the rest of his life as a political hot potato and adventurer. He went to a boarding school in Yorkshire, held military command under Bolivar and was a member of the Papal Zouaves, who had the best uniform in 19th century Europe, bar the Swiss Guards.
Jacques-Victor Henry, Prince Royal of Haiti - son of Henry Christophe, self-proclaimed King of northern Haiti. His dad died in 1820 but he didn't inherit the throne because Henry's governance was crap - he kept the old slave plantations running, sans the slaves - and he'd only managed to keep the north with the strength of his personality. J-V and most of the high command were butchered in their own Palace within 10 days of his father's death. He was 16 at the time.