Why is it that Goten and Trunks don't have tails? I don't believe I've ever seen Goten or Trunks with tails, which doesn't quite make sense, seeing as how Gohan had a tail at his birth, and was also half saiyan half human. From what I've read, it's assumed that they were cut off at birth, but I'd like to know officially if that's the case, since the articles I read had no sources. And I'm pretty sure Saiyan tails normally grow back. Is there anywhere in DBZ that they mention the permanent removal of Goten's and Trunks's tails?
A common theory is that Akira Toriyama just didn't want to / forgot that Saiyans had tails. This wouldn't be surprising as Akira makes several other errors/omittances in the series.
Here's an interview segment from him talking about Goku's tail:
Is it true that Goku’s tail was a nuisance?!

It’s true. (laughs)
Goku was originally an actual monkey in the initial sketches, after all. My editor told me, “Without a tail, he has no distinguishing traits,” so I added a tail.
That tail I added was such a nuisance when I was drawing, I couldn’t stand it… so I immediately thought up an episode where his tail gets cut off. (laughs)

It wouldn't be surprising if having gotten rid of the tail that he so hated, he didn't really want to reintroduce it into the story again, so rather he left Trunks and Gohen without one.