Not every witness against the mob who has to go into hiding with a price on their head is just someone who happened to be in the wrong place at the wrong time;far from it. Many mob witnesses were mobsters themselves who were caught and grassed to escape a death sentence or a lengthy prison term,and by no means all are willing to go straight when in hiding waiting to testify. This one is up to his old tricks, picking fights with ordinary people and beating them up, being bad tempered and aggressive,and committing crime at every opportunity. The PCs have to babysit him, stop him from ending up getting arrested by the local police, and of course make sure that the Mob's torpedoes don't track him down, and defend him if they do despite his personal dislike of them and their just as strong dislike of him.
2-Off His or Her Own Back
Either there is no such thing as formal witness protection, or this person dislikes or does not trust what is offered. He or she has gone into hiding by just adopting a new name informally, but without any references or even a bank account, cannot get any decent job and is forced to either beg, steal or work informally in the black ecomony for not much money. Either homeless or living in a dirty shack, his or her clothes dirty through lack of washing, he/she knows something that the PCs need and will only tell if able to tag along with them. Do the PCs just torture the infomation out of him or her, do they use blackmail, offer a large reward, or let this smelly, dirty, poor person come on their quest with them?
Be it through bribes, their own stupidity or sheer bad luck the person who the PCs are trying to protect has been found by large numbers of bad guys, and the PCs must stage a fighting retreat whilst keeping their person safe and killing or injuring as many of the foes as possible in the twisty alleys of town.
Complications if desired
-The Bad guys know the area as well or even better then the PCs, and rather then shaking them off the PCs could get lost or even split up.
-The Bad guys have enough political clout to enlist the well-armed and trained City Guards on their side.
-The person that the PCs are protecting lied to them and is in fact a very nasty person who fully deserves his or her fate. How will the PCs react if they find out about this?
4-Fleeing from Battle
The battle is clearly lost and the soldier (or PCs, as this could work as a mini-roleplay all by itself) is fleeing the battlefield rather then join the
dead for a cause that is clearly lost. It is not necessarily cowardice that is the cause of the retreat, all the formed units have been overwhelmed and anyone who stands fast is quickly going to die or at the very least end up serving time in a very unpleasant prisoner of war camp. Depending on the time period there may well either be charging horses and volleys of arrows to worry about as well as the rampaging infantry, or bullets wanging about all over the place and tanks chasing their beaten foes. If the general is particularly cruel then there may be an extra hazard; blocking detachments ordered to kill anybody of their own sides who dares to retreat.
The PCs have somehow managed to anger a full size Dragon and now the enraged leviathan is aloft on it's mighty wings and trying to track them down. If they hide in villages or even cities it will threaten to burn them down if the PCs are not handed over to it within a certain time frame, whilst on the roads they will be easily picked out. Perhaps if they can hide for long enough the Dragon will lose interest;perhaps Dragons are very territorial and if they can enter the territory of another,larger, Dragon, the first will not follow them. Or the whole quest is about finding a magical weapon such as The Black Spear or potent spell that really does have the power to kill a full grown Dragon. Even if they do kill it they may have to flee again in the short term from any Draconian parasites that were living on the Dragon and now crawl off in large numbers and vengefully attack the PCs who killed their host.
6-Running from the Law (1)
The person being chased by the police (or the PCs) are innocent of the crime and have either been deliberatly fitted up by a bent or racist police officer or whoever did the dastardly deed made it look like it was someone else who did it. Either the judicial system itself is unfair or corrupt, or there would be a long wait in prison before trial, or perhaps if caught a murder in prison will be arranged. So there is no question of just turning oneself in and letting a trial sort things out;one can either make a straight run for the border, or try and expose the frame up whilst being hunted down by the police or the local lynch mob (or both if the crime is bad enough) and expose the real criminal behind all the trouble.
7-Running from the Law (2)
The person being chased by the police (or the PCs) have a simple reason not to give up...he/she/they really did commit the crime in question and it is one with a very severe punishment if caught and convicted. The PCs could be chasing the guilty offender;or they could belong to the Thieves Guild or it's equivalent and get away with their booty. Capture is not an option unless one wants to face the headsman or something worse, like the feared Hellgate Prison. The border/safehouse is only X number of miles away, but it won't be easy to get there with law enforcement/bounty hunters/bands of vigilantes/all three hot on the trail,eager to claim the reward.
After an earthquake or an encounter with Ma-O the Water Deamon a massive tidal wave more then seventy feet high is sweeping in towards the land and the PCs must run for their lives. The first sign of the incoming wave is when the sea seems to gurgle out as if somebody has pulled a plug out, exposing coral, wrecked ships and other such things on the seabed. Wise PCs will heed the watery warning and Get Out Now or if that is impossible,climb into a beached boat and pull up the anchor. Not long afterwards the wave will arrive,sweep over the beach and break, sending walls of water through the streets of the nearby town and flooding it. So big is the wave that it could sweep at least a mile inland, filled with debris of every description. Even when it sucks it's way back to the sea the danger is not over yet;other waves might follow;unspolied water and food will be scarce;there may well be looters and some of the braver or stupider ones might try to rob the PCs;there will be dead and slowly decaying bodies that must be either cremated (but all the wood will be wet) or buried in hastily dug graves before they start to spread disease.