Saints Row is indeed a sandbox game where you have the option to do the main campaign missions, perform side-tasks to gain respect which allows you to do the main story missions or you have to option to get in a car, plow into a building and introduce a rocket to the back window of said car. Now of course this has always been a staple of the sandbox/ open world genre and Saints Row makes it really, really fun.
The main story revolves around the Third Street Saints, a local gang who control an area called Saints Row in the fictional city of Stillwater. You play as a new recruit who has to earn his stripes to get into the Saints and eventually move up in the ranks of the gang. The Saints want to take over Stillwater, but so do 3 other factions who reside in the city. This is where the main story begins. Handling various tasks to sabotage the other gangs allowing the Saints to move onto their turf eventually eliminating the other factions completely and taking over Stillwater.
The characters are developed well and although there is limited backstory given you figure out who they are early on in the game and become close with them throughout. Julius and Johnny Gat are two of the most creative characters even established in a video game. Gat is a hothead who is extremely handy with anything that involves bullets while Julius is the Samuel L. Jackson type leader of the Saints who takes you under his wing and shows you the ropes of gang violence.
The missions are creative although do not require much thinking for the most part and the final events of Saints Row definitely leave room for a sequel and hopefully more to come. Saints Row is a must buy for any Xbox/PS3 owner.