There are a number of theories concerning Tutankhamun's family. We know that he married one of Akhenaten's daughters, Ankhesenamun and that there is no record of them having had any children.

As for his parents, things start to get complicated. There are a number of proposed possibilities.

Akhenaten and Nefertiti
This is unlikely, the surviving records state that Nefertiti and Akhenaten had 6 daughters, but no mention is made of a son

Akhenaten and Kiya
After Nefertiti disappeared from history, a new Queen was mentioned, the lady Kiya. The dates do not appear to line up for Kiya to be Tutankhamun's mother, unless he was born while Nefertiti was still around.

Smenkhkare and Meritaten
Smenkhkare is a figure of some debate with questions about who he (or she) was, if in fact they ever existed. If there was a long coregency between Akhenaten and Smenkhkare then it is possible that Smenkhkare was Tutankhamun's father.

Amenhotep III and Tiye
This is unlikely unless the present chronology is very wrong. Tutankhamun was 9 when he ascended the throne, and as Akhenaten reigned for around 18 years, so if Amenhotep III was his father he would have had to have had a 9 year coregency with Akhenaten.