I've attempted this without much success. The faults could easily lie with my skills as a DM but I feel the players have a large role as well and they dictate how much fun can be had with such a format.
I initially had each player create a solid backstory with several elements that could be tied to the game world. In addition I requested a general goal or two the character would like to achieve. When getting such things from all the players, this essentially opens up a ton of side-quests that can be explored.
Unless you're great with working on the fly. Sandbox games can easily suffer from lack of excitement. Sessions may involve you simply stalling for time (needless encounters) until which point you think of something interesting to do with what the PC's are trying to accomplish.
Expect the unexpected. You can easily establish several story hooks for a party to explore...but they'll often latch on to a certain detail and go from there. In my case, anything that sounds like possible treasure was always more important than an act of kindness with no specific time limits in place.
Personally, I enjoyed running this style of game, but in the future I'd recommend running it in a world the party knows. Mine was all custom. People in my group have all played Dragon Age for example. Establishing any kind of story in a world like that seems like it would make for a great sandbox as the players have a good idea of the world and its politics/expectations.
The main benefit of a sandbox game is that it only gets better with time. Once you get over the initial hang-ups, the PC's will hopefully come up with more and more ideas themselves to drive the story. All their actions have longstanding consequences, and this aspect continually makes the game potentially great, especially when you create quests with strong moral choices.