Who is Ichigo's Father, Isshin?
Isshin Kurosaki used to be a Shinigami of an unknown division and rank. According to bleach.wikia.com:


  About twenty years ago, he ceased being a Shinigami, losing most of his powers.


He still has a shikai, which he uses during the Fake Karakura arc.

Spoiler:


  Ichigo also has Quincy powers that have been implied to be related to his mother. If Ichigo's mother was a Quincy, Isshin may have known.