Darren Melrose, 18, Jordan Parry, 16, Billy Jo Revie, 16, and a 16-year-old girl from Linwood, Renfrewshire, who cannot be named for legal reasons, are alleged to have broken into the Clutha, in Stockwell Street, on December 17 and stolen alcohol and charity tins from the wrecked interior.
They appeared separately in private yesterday at Glasgow Sheriff Court, each facing a charge of theft by housebreaking.
The four are accused of stealing a "quantity of alcohol and cash from charity tins" from the pub.
Melrose, and Parry, from Sauchiehall Street; Revie, from Carmichael Street, Govan; and the 16-year-old girl made no plea or declaration.
Melrose, Parry and the 16-year-old girl were remanded in custody. Revie was granted bail.
The Clutha tragedy happened on November 30 when a police helicopter with a pilot and two police officers on board plummeted into the packed pub in Stockwell Street.
It has not yet been established what caused the helicopter to fall from the sky, although investigators said initial evidence ruled out major engine or gearbox failure.
The first nine victims of the tragedy were pilot David Traill, 51; Constables Tony Collins, 43, and Kirsty Nelis, 36; and customers John McGarrigle, 57; Mark O'Prey, 44; Gary Arthur, 48; Colin Gibson, 33; Robert Jenkins, 61; and Samuel McGhee, 56.
The 10th victim, Joe Cusker, 59, of Cambuslang, died in hospital almost two weeks later.