Much to my surprise there's actually a Wiki link and whole write up on this subject:
"Bennifer", a portmanteau, was the nickname given to the celebrity couple Jennifer Lopez and Ben Affleck by Affleck's friend, Kevin Smith. The couple, who met on the set of their mega-flop Gigli, received a great deal of media attention, similar to that experienced by Elizabeth Taylor and Richard Burton in the 1960s. Their relationship spanned eighteen months and included a much-hyped engagement, a 6 carat (1.2 g) Harry Winston diamond engagement ring, an aborted wedding, and a prolonged breakup, culminating in their split on January 20 2004, with both blaming media attention.
They extravagantly flaunted their love affair with public displays of affection and multi-million-dollar gifts, including Bentley cars and huge diamond rings. "Bennifer" is sometimes also used to refer to Affleck and his current wife, Jennifer Garner, though "Garfleck" and "Bennifer II" are also used. Some media outlets referred to their first daughter, born December 1, 2005, as "Bennifer Jr."