I haven't done much GMing, but it's always fun for Mr. Johnson to pretend to have a different affiliation. Especially handy for someone from Horizon, in case they can outsource Runners Seeking Vengeance to another megacorp. Ares or S-K is handy for "Instead of nuyen, I'll pay each of you with new guns and equipment," and I like bringing in Karma-rich runs from Concerned Citizens who probably aren't harbouring a terrible secret.
As for targets, I would like to schedule runs against stuff like Aztechnology or Humanis, but I have been kicking around an idea for one crime syndicate hiring runners to attack a different one, while implicating a third. I'd probably need a long-term group for that. One that'd find a mob war exciting.
I did run a seat-of-my-pants one-shot where the runners were paid to extract someone who was secretly a monad, and got caught up in an all-out, spells-and-bullets-everywhere exchange between some shedim and bug shamans who'd unintentionally scheduled their evil demonstrations for the same time and place. It was all very tongue-in-cheek.