|Players stitched this explored area together from the maps I would give them|
This linear nature also means creating regions of sandbox encounters is both easy, but also fragile. I want to go over the process to show how this is a problem and also why I hope 5E solves this.
Here's how I do it:
You have your base of operations for low level characters. It's assumed that threats to this base are easier to handle by low level characters because the town would have either dealt with mid level threats or would have been wiped out already. It's also good to have a power base of "good guys," who can keep the mid level stuff in check, but also have some indifference towards the plight of the PCs. I have druids, rangers, and the forces in town keep the local threats in check, while some powerful boundary magic thrown in gives some justification for why a civilization hasn't been overrun. My good guys are actually neutral, have plans and designs of their own, and generally don't want PCs upsetting the balance. Really, don't rock the boat or bad things will happen. And they did rock the boat. And bad things did happen to the town.
So here we have a region of low level stuff, enough to get the PCs to that sweet spot of around 5th level or higher. They might be told not to go over the hills or not to explore the ocean because of the danger. Eventually they get their courage (and levels) up and take the plunge.
My mid-level regions (encounters for 5th-9th level characters, more or less), are far more dangerous. They're characterized by a balance of power. There probably aren't any good guys in this wilderness, but there are tribes of neutral and evil humanoids kept in check by bigger monsters. Evil wizards are kept in check by dragons. Combinations of several forces live on the edge of war with their own problems and motivations.
This allows PCs to allie with groups, gain passage for favors, take on missions, or whatever. Going in and squashing a tribe of goblins or killing a dragon is likely to have repercussions. Who was that dragon keeping in check? What kept the goblins tribes from invading the town? Perhaps the legion of undead from the lich kept the big bad guy from overrunning the island (they did). The enemy of their enemy is their friend. This was hard fought wisdom that had them questioning the situation every time they came into a new power dynamic. You know, role playing.
Deeper into the wilderness you can get even more epic, with lost cities, fallen civilizations of cyclops or giants, powerful magics run amok, and mountainous regions that are generally inaccessible (a good boundary). In my campaign, the mountains hold treasures and secrets that all the powers on the outskirts would like to control. That is, if they could conquer the center from the periphery.
This is all very linear. However, players don't explore in a linear fashion, in concentric circles out from home. They tend to do that in the beginning and then they start picking a direction. This leaves a lot of content on the table that will never get used, a reason why a key sandbox rule is to not go nuts designing everything. Again, the linear power levels of Pathfinder PCs means the sandbox becomes its own "adventure path" whether you like it or not. Some stories will fall by the side as they obsolete them with their power level.
The hopes of D&D 5th edition is we see a flatter power curve. The promise that a tribe of goblins can kill high level PCs is one sandbox DMs should hope is true. I see some of that now as I design those mid level encounters. The higher CR monsters don't seem significantly more powerful than low level guys. It's actually deceptively deadly when I run it through this most excellent online encounter calculator. Give a necromancer a couple of skeletons or a hobgoblin some goblin mooks, and suddenly the encounter goes from average to deadly as the action economy plays a role not seen in D20.
If this is true (and I have about 4 hours of D&D 5 play experience at this point), it will make D&D 5 the ideal sandbox game system. Just as Ken points out that back in the day, a solid sandbox campaign could go on for a decade or more with the same party. Let's hope that's true with 5E.