Easton's 1897 Bible Dictionary:

Abimelech
   my father a king, or father of a king, a common name of the
   Philistine kings, as "Pharaoh" was of the Egyptian kings. (1.)
   The Philistine king of Gerar in the time of Abraham (Gen.
   20:1-18). By an interposition of Providence, Sarah was delivered
   from his harem, and was restored to her husband Abraham. As a
   mark of respect he gave to Abraham valuable gifts, and offered
   him a settlement in any part of his country; while at the same
   time he delicately and yet severely rebuked him for having
   practised a deception upon him in pretending that Sarah was only
   his sister. Among the gifts presented by the king were a
   thousand pieces of silver as a "covering of the eyes" for Sarah;
   i.e., either as an atoning gift and a testimony of her innocence
   in the sight of all, or rather for the purpose of procuring a
   veil for Sarah to conceal her beauty, and thus as a reproof to
   her for not having worn a veil which, as a married woman, she
   ought to have done. A few years after this Abimelech visited
   Abraham, who had removed southward beyond his territory, and
   there entered into a league of peace and friendship with him.
   This league was the first of which we have any record. It was
   confirmed by a mutual oath at Beer-sheba (Gen. 21:22-34).

     (2.) A king of Gerar in the time of Isaac, probably the son of
   the preceeding (Gen. 26:1-22). Isaac sought refuge in his
   territory during a famine, and there he acted a part with
   reference to his wife Rebekah similar to that of his father
   Abraham with reference to Sarah. Abimelech rebuked him for the
   deception, which he accidentally discovered. Isaac settled for a
   while here, and prospered. Abimelech desired him, however, to
   leave his territory, which Isaac did. Abimelech afterwards
   visited him when he was encamped at Beer-sheba, and expressed a
   desire to renew the covenant which had been entered into between
   their fathers (Gen. 26:26-31).

     (3.) A son of Gideon (Judg. 9:1), who was proclaimed king
   after the death of his father (Judg. 8:33-9:6). One of his first
   acts was to murder his brothers, seventy in number, "on one
   stone," at Ophrah. Only one named Jotham escaped. He was an
   unprincipled, ambitious ruler, often engaged in war with his own
   subjects. When engaged in reducing the town of Thebez, which had
   revolted, he was struck mortally on his head by a mill-stone,
   thrown by the hand of a woman from the wall above. Perceiving
   that the wound was mortal, he desired his armour-bearer to
   thrust him through with his sword, that it might not be said he
   had perished by the hand of a woman (Judg. 9:50-57).

     (4.) The son of Abiathar, and high priest in the time of David
   (1 Chr. 18:16). In the parallel passage, 2 Sam. 8:17, we have
   the name Ahimelech, and Abiathar, the son of Ahimelech. This
   most authorities consider the more correct reading. (5.) Achish,
   king of Gath, in the title of Ps. 34. (Comp. 1 Sam. 21:10-15.)


Hitchcock's Bible Names Dictionary (late 1800's):

Abimelech, father of the king