I don't agree that sandboxing and railroading are at two opposite ends of the spectrum - although the issue is complicated by the fact that these are contested notions.
By "railroading" I mean something like what most of the posts here seem to have in mind - a game in which the GM makes most of the choices about how encounters and PC actions will resolve. Maybe the players get to make the local tactical decisions - do we win the fight with a lightning bolt or a great-axe? - but the GM ultimately decides how things unfold. Extreme versions of this are the GM "cheating" to make sure that the upshot of an encounter is what s/he has planned in advance.
By sandboxing I mean an exploration game - the GM has created a world with lots of places and NPCs in it, random encounters to add a certain verisimilitudinous dynamism, and the players get to explore that world using their PCs as their vehicles. The negative stereotype of a sandbox is that given by the OP - the GM describes the tavern, or the city square, in which the PCs find themselves and then asks "So, what do you do next?"
I prefer a game which is neither sandbox nor railroad. The essence of my preferred approach is for the GM to create strong - even compelling - situations, which the players are then free to resolve (using their PCs as vehicles) however they like. The way to make a situation compelling, for a given group of players, is to make sure that it evokes game elements or thematic material that those players are interested in.
One way to do this, and the way I tend to rely on the most, is to exploit PC backgrounds, or aspects of PC personality that have been displayed in prior play. So if there is a cleric of the Raven Queen in the party, then I will tell the players that their PCs notice a statue down an alleyway that looks like a shrine to Orcus. Or if a player has expressed a desire to take the Demonskin Adept paragon path, then I will create situations in which demons, or other abyssal forces, play a prominent role.
Another way to do this is simply to use engaging NPCs. Provided that your players are prepared to buy into some in-character roleplay, then you can get their PCs quite deeply enmeshed in a situation simply by having an NPC speak to them, perhaps lead them somewhere, all the while conversing with them in a way that the players are finding fun at the table.
The following
quote from Paul Czege really captures, for me, how I like to GM (although the way he expresses it is a lot more hardcore than my game - I run a pretty laid-back fantasy RPG):
Let me say that I think your "Point A to Point B" way of thinking about scene framing is pretty damn incisive . . .:
There are two points to a scene - Point A, where the PCs start the scene, and Point B, where they end up. Most games let the players control some aspect of Point A, and then railroad the PCs to point B. Good narrativism will reverse that by letting the GM create a compelling Point A, and let the players dictate what Point B is (ie, there is no Point B prior to the scene beginning).
I think it very effectively exposes, as Ron points out above, that although roleplaying games typically feature scene transition, by "scene framing" we're talking about a subset of scene transition that features a different kind of intentionality. My personal inclination is to call the traditional method "scene extrapolation," because the details of the Point A of scenes initiated using the method are typically arrived at primarily by considering the physics of the game world, what has happened prior to the scene, and the unrevealed actions and aspirations of characters that only the GM knows about.
"Scene framing" is a very different mental process for me. Tim asked if scene transitions were delicate. They aren't. Delicacy is a trait I'd attach to "scene extrapolation," the idea being to make scene initiation seem an outgrowth of prior events, objective, unintentional, non-threatening, but not to the way I've come to frame scenes in games I've run recently. More often than not, the PC's have been geographically separate from each other in the game world. So I go around the room, taking a turn with each player, framing a scene and playing it out. I'm having trouble capturing in dispassionate words what it's like, so I'm going to have to dispense with dispassionate words. By god, when I'm framing scenes, and I'm in the zone, I'm turning a freakin' firehose of adversity and situation on the character. It is not an objective outgrowth of prior events. It's intentional as all get out. We've had a group character session, during which it was my job to find out what the player finds interesting about the character. And I know what I find interesting. I frame the character into the middle of conflicts I think will push and pull in ways that are interesting to me and to the player. I keep NPC personalities somewhat unfixed in my mind, allowing me to retroactively justify their behaviors in support of this. And like Scott's "Point A to Point B" model says, the outcome of the scene is not preconceived.
How does it feel? I suspect it feels like being a guest on a fast-paced political roundtable television program. I think the players probably love it for the adrenaline, but sometimes can't help but breathe a calming sigh when I say "cut."
My game featuers more "scene extrapolation" then Czege's does (although I probably use hard scene framing more often than a lot of ENworld GMs). But the basic idea - that the GM metagames very heavily by deliberately constructing engaging situations,
and then leaves the players to choose how to resolve them - I find quite powerful. It is different from a sandbox, because it is not about the PCs exploring a pre-existing world, but rather the GM presenting a world that is built precisely to engage the players.
I also use some of the other techniques Czege describes, like filling in the details of NPC motivations and other parts of the backstory
during the cours of play, in order to keep driving the game forward in an engaging fashion. For me, this is the other key difference from a sandbox. When the players are exploring and engaging with the world, that world is being built on the fly
to keep them engaged and keep them on their toes. For me, this is the best way to have a non-railroaded, player driven game that nevertheless is focused on the PCs achieving goals that are meaningful both for them and for their players.