I'm a bit enthralled with the concept of Tarrasque-as-natural-disaster, and I'd like to try running a campaign around that idea. These are the plot seeds I'm mulling over at the moment:

1. The players have advance warning of the Tarrasque's arrival and must
   1. Find a way to change its path (such as luring it elsewhere) so their city is not destroyed, and/or
   2. Seek and secure the alliance of a being or beings powerful enough to fend it off, such as an ancient dragon.
2. The Tarrasque has already arrived by the beginning of the campaign and the players must
   1. Help civilians survive the rampage/mitigate the damage done, and
   2. Help rebuild the town after the Tarrasque has left, which would include fending off looters, etc.

Thoughts on either of the above concepts? How have you used the Tarrasque in your games?

Depends on what sort of game you want to run. Do you want to play the Tarrasque as an unstoppable force of nature, which the characters have no hope of fighting? Go for the second, but if you want to give the characters even just a sliver of a hope that this thing might actually be fought, go for the second.

It's also a bit about the time scale of the story. The first one is a bit of a race against the clock, with the characters desperately trying to succeed on their mission before it's too late. The second one is more a bit of both. Start of with every second counting, every second they waste, the tarrasque claims another victim, but after the rampage, it can slow down a bit, letting the players breathe, and slowly but surely rebuild what was lost.

I think a lot depends on what level the players are.

Levels 1 - 4: The tarrasque would simply be a background event. The players wouldn't get near it, unless they want a first-night TPK. Instead, a good party could focus on escorting townsfolk to safety, and fending off the opportunistic bandits that might take advantage of the chaos to loot and pillage. Or, a less good-aligned party might themselves take advantage of the chaos to loot and pillage. Their reward is whatever they find (if not good), or food, prestige, and maybe a healing potion (if good).

Levels 5 - 10: The party still isn't fighting the tarrasque directly. Rather, they could be searching for an artifact that might help weaken the creature. They could be trying to get ahead of it's path to warn and evacuate people. For the more role-playing oriented, they could be trying to negotiate for assistance from a dwarven clan, or a powerful dragon. Their reward is whatever other treasure they find along the way. 

Levels 11 - 16: Same as 5-10, but more difficult. they might also learn that a certain wizard conclave summoned the tarrasque, so they have to find those wizards and get the information needed to defeat or banish the beast! Also, it's at this tier that the players might first face the tarrasque directly. But not on their own! Perhaps they're part of a coalition army from across the countryside that is cooperating against this common enemy. Their reward is whatever other treasure they find along the way, plus social and political rewards from the various units or kingdoms they recruit into the war effort.

Level 17 - 20: The players are the tip of the spear, leading the coalition army in battle against the tarrasque. Their reward is, well... probably.... a glorious death in battle. Or, maybe, their reward is land, a castle, leadership of an army, taxes, and a considerable share of whatever shiny bits of treasure they can cut out of the tarrasque's gullet and/or lair. 

That being said, I've always felt that The Tarrasque, as it's listed in the stat block, is too weak. I know! I know! It's not weak! I just mean... I feel like The Tarrasque is meant to be one of those things that can't ever really be defeated. It literally IS a force of nature. Honestly, ask yourself... "how many times would you have to hit a tornado with a sword before you can be assured that no tornado will ever again strike your village?" It doesn't work like that. You can't "beat the tornado". Well... you can't beat the Tarrasque. 

But that's just my two copper pieces.  

Great breakdown, Tayn! I definitely want to keep things at the lower levels. I agree with you that the Tarrasque isn't "beatable" - it's only survivable. If this were an epic-level game I'd probably implement the mechanic from 4E that reducing it to 0 HP just causes it to enter hibernation mode, but since the players won't be directly facing the Tarrasque it probably won't come up.

I'm thinking that the Tarrasque will narratively be almost the same as a major hurricane: it's a major destructive force that is coming towards land, but fortunately people have some advance warning and can evacuate its predicted path. The PCs will be tasked with facilitating the evacuation. The have X number of days to travel Y miles away; they'll have to roll a Survival check at the end of each day to ensure they're staying on pace, with the DC going up or down depending on whether they did anything besides traveling that day. Complications they will face:

1) Civilians who don't want to evacuate; they think they can "weather the storm" in place. PCs can try to persuade civvies; if that fails, will they leave the civvies to their fate? Forcibly remove them?

2) Looters/bandits preying upon the evacuees.

3) Physical impediments on the planned evacuation route (bridge out, rockfall, etc.). Should they find another route? Try to clear the impediment? Which one will cost them more time?

4) An evacuee is missing; their family is frantic and insists the PCs help search for them. Do the PCs relent or do they press on ahead?

Any other ideas are welcome, too.

Hibernation! Exactly. When it reaches zero hit points it doesn't die. It just sinks down into the earth, beyond the reach of those fighting it. It melds with the earth for some specified time. Maybe a century and a day. Maybe 1000 years. Maybe until the Zenith Star next rises through the eastern window of the Sun King Temple on the night of the summer solstice. Something like that.  

Combat missions are standard fare in D&D. And your plan will have plenty of chance for that. Not only will the party have to protect the civilians from looters and bandits and whatnot. But the rise of the tarrasque will upset a major geographical area. So everything that lived in that area will now be on the move, IN A HURRY! Animals will be migrating in abject fear! That's a danger! Any bad guys who lived in that area might now be in YOUR area! And not just animals will be migrating away from the tarrasque, monsters will be too. You'll have not just deer, and wolves, and pheasants, and skunks fleeing the tarrasque, there could be gnolls and manticores and hill giants and maybe even a dragon! You won't just be fleeing the tarrasque, you'll be fleeing the absolute meat grinder of monsters that got stirred up in its wake!

Oh. And maybe the tarrasque is some legendary harbinger of death. Maybe there's a necrotic element to it. Maybe a certain percentage of creatures it kills rise an hour later as zombies. 

Whatever the side-effects are, they're at least as much a danger as the tarrasque itself. And even once the tarrasque has been beaten, and goes back into hibernation mode - YOU'RE NOT DONE! You'll still be sitting in a world that has just been turned upside down, with monsters running rampant, with thousands of scared and hungry refugees on the roads. And a significant portion of the soldiers and local militia and healers who would normally deal with such a problem are gone, because they just died fighting the dang tarrasque! 

Heck, defeating the tarrasque might even be the easiest part of the campaign.

Putting the world back together again afterwards - THAT'S the REAL challenge!