Wow, some people in this topic who have really missed the point of Saints Row: The Third. Don't bash it for being unrealistic - its MEANT to be over the top, completely impossible fun. Thats what makes Saints Row so great and fun. This is the main story of SR:TT since no-one else has mentioned it:
The Saints are now a massive gang now, very famous and they're bored one day and decide to rob a bank. The robbery fails after Josh Birk (an actor who is accompanying the Saints to prepare for his movie role in a Saints movie) accidentally triggers an alarm. SWAT teams come and arrest you. Phillipe Loren and his secretaries Viola and Kika DeWynter rescue you from the jail in his plane, and it turns out that Phillipe is the leader of the Syndicate - a trio of gangs (the Morning Star, led by Philippe; The Deckers, led by Matt Miller and The Luchadores, led by Killbane) who are all connected and pretty much rule Steelport.
So then this mission happens. Basically Phillipe offer to either kill the Saints or force the Saints to become part of the Syndicate. The Saints aren't having this because they're the fucking Saints, they're not bowing down to those motherfuckers, so they jump out of the plane and fight Morning Star members on the way down to Steelport.
Eventually the Saints move from Stilwater to Steelport, and will take down the gangs and a group which is like Ultor but twice as brutal - STAG. They have hoverbikes and VTOLs which shoot lasers and missiles. But yeah, you're the leader of the Saints - you can take them all on, with dildo bats, apoca-fists and a shit ton of other weapons and vehicles, which are all customisable. Plus possibly the best character customisation in any game, ever.
So yeah. Best game ever?