The author of this site (JB), is a big proponent of Sandbox games over Story Games (a subject I've spoken on many times before, so I won't repeat... much). What I do want to reiterate is that I don't think Sandbox and Story are mutually exclusive—at least, not if stories are done right (i.e. you give the players a situation and let them SHAPE the story, rather than just run it down a single 'rail').
The fact of the matter is, I wouldn't have it any other way. Hands down, the BEST moments in my campaign have been when the players come up with some idea out of left-field that just stops me dead in my tracks. I mean, I like to try to think of all kinds of 'contingencies' when I'm planning out an adventure, but I'd say that about half the time they come up with something I hadn't anticipated and I'm left scrambling. Thankfully, I enjoy scrambling (even if I do sometimes have to call a five minute break to figure out what the heck is going to happen next).
Some prime examples of these 'surprises' (from my main Vermillion campaign) include:
Bob's plan to sell the Imperials a broken prototype shield belt.
Oman's 'omega particle' dectector.
Adren's 'hobby' of redeeming villains rather than capturing/killing them.
Horatio's...well, just about every plan he's ever come up with.
Arianne's trip to 'chez domination'.
Hugganut's Sabbacc playing skilz.
Oman's plan to send an alien invasion fleet into another dimension.
Bob's water-bucket-cloaking-device analogy.
Jared's attempt to 'disbelieve' a Rancor.
Adren punching Arianne.
Bob explosively decompressing a chamber containing hundreds of Stormtroopers (as well as himself and a couple others in the party..)
Arianne attempting to shield a cruiser from the (2nd) Death Star with her Gunship (ballsy move, even if a bit futile)
The team 'accidently' blowing away an innocent secretary while on a black op infiltration mission.
The team attempting to escape a high-rise by cutting down through 47+ levels with a lightsaber (while on the same black op infiltration mission...after it had already blown up in their faces)
Oman and Martell suddenly breaking off from the rest of the group to conduct their own investigation of "The Game Chambers of Questal"
There are many, many more of these 'surprises' and as you can tell, they were very memorable. All of them happened in what I would term a 'story-based' campaign. It is pretty evident (to me at least) that 'story' does not equal 'railroad'—at least not how I run it. The surprises are what give life to the game. They are what I look forward to the most. They are the essential element in any RPG—and they are NOT curtailed just because there is a plot involved in an adventure or gaming session.