I don't know if they had a tail when they were born. But if they did then they probably had it cut as a baby. Chichi always wanted a normal son. When she found out Goten could also turn into super saiyan, she cried... so that could be why. And while Trunks was a baby, Vegeta didn't really care much for him and so Bulma probably thought it'd be better off since there was really no need for it, too. And it could also be that they didn't want their kids turning into giant monkies just in case they see a full moon.. I don't know, maybe the same goes with Bra... And Pan, she's a quarter human so she probably never had a tail.
Chi Chi and Bulma must have cut them off as soon as they were born because of the affects it has to them.... I am sure nobody would want 2 Sayins in there Gorilla form running around the town
Gohan had a tail because it was at the start of dragon ball z then he turned into a great ape while training. Goten and Trunks don't have tails because they were possibly cut off to prevent transforming into great apes. Same for Bulla ana Pan