One of the first science fiction books I read which seemed to make my synapses fire off all at once in a cognitive supernova was William Gibson's Neuromancer. In it, Gibson presents both AIs Wintermute and Neuromancer as complementary halves of one family's mega-corporation. In essence, by unifying both the AIs the corporation started by the Tessier-Ashpools, their corporation--and by extension, their family influence--would become immortal.
Sort of like the literalization of a corporation's "going concern."
As can be expected, the AIs here are vast demi-godlike entities, alien and threatening by turns.
Re-reading Naomi Kritzer's "Cat Pictures Please" the AI there is more interested in finding ways to please or help different people who post cat pictures online. It's a cute and very positive story. It also offers a clever explanation for why cat pictures are one of the currencies of current internet culture. The story is told from the point of view of the AI...