In the words of Akito from 'Martian Successor Nadeshiko" (an anime about 10 years old now) "What's wrong with running away?"
In games, I think this is actually a valid question.
RPGs are particularly bad for making the player obligated to kill or surmount any obstacle in their way. In fact, going out of your way to kill stuff is almost always beneficial, as it means more xp points, so higher levels and better abilities, as well as more items and money. One of the only things I dislike about Chrono Trigger, which in all other respects is so good that it's firmly placed in my top 5 games of all time, is that though you CAN avoid monsters, if you take advantage of this ability, you won't reach good levels and will just get hammered by bosses and unavoidable encounters. Therefore, having avoidable encounters becomes even weirder than unavoidable random encounters from Final Fantasy games, because you deliberately run at and attack any monster you see! Come to me, precious bags of exp! hahaha! So rather than 'hapless adventurer attacked by the minions of darkness while trying to achieve my goal!' it's more like I'm 'brutal hunter and slayer of anything that gets close enough that I can see it!'
But wait, wait. Realitically, you avoid fights, right? Even a soldier in a war zone isn't encouraged to go out of his or her way looking for trouble. If I were to see a rowdy looking gang on the other side of the street, I wouldn't run into their midst to beat them up. Generally, you only fight someting if you feel the reward outweighs the risk, or the risk of not dealing with it outweighs the risk of fighting, or if there's simply no other option.
In an RPG, the reward almost always outweighs the risk, except in clever examples like the 'T-Rexaur' monster early in FF VIII, which is so powerful when you're at low levels that, when you see one, party member Quistis says, 'Remember, Squall, sometimes it's better to run!' and later on, a boss fight revolves around running from the monster. You do get a bonus for beating it, but you would have had to do a lot of level grinding and item hunting, and it's not the standard way to beat the boss. The standard way is to run from it, staving it off only when needed, until you reach the shore where your friend shoots it to pieces with a ship-mounted machine gun. In most RPGs, however, you will likely aquire new weapons, armour and items as well as experience points from defeating monsters.
In fact, the whole act of killing things and looting their bodies is taken so much for granted in RPGs and FPS games generally, that you stop thinking about how it's really not that nice. I mean, if we think realistically here, it's highly unlikely that an enemy will have a better weapon than you have, unless they're carrying something very special, or it's ammunition. Their armour shouldn't always fit you, their weapons and items shouldn't nessesarily interest you, in fact think about this scenario...
Somebody comes at you with a broken bottle to attack. You deck them because you can't do much else, they had you cornered. Do you go through their pockets and steal their money, car keys, penknife and tesco coupons? Most people wouldn't. In an RPG, even pious knights seem to have no problems with stripping armour off defeated foes to wear! This is partially because RPGs have this idea of getting 'better' armour, and for ease of play, all armour fits all characters and weapons and armour compare in simple, mathamatical terms as 'better' or 'worse'.
Why can't we just run away from things? Why are we always forced to fight them?
What would happen if you made a game in which:
The character doesn't need any new armour s/he is perfectly happy unarmoured because they can move faster and more easily. Besides, maybe it wouldn't fit them anyway?
The character doesn't need to nick everybody's swords, s/he has a weapon, just in case, and they don't need any more weighing them down.
The character doesn't like hurting or killing people and would prefer to just stay out of the way.
It was realistically hard to fence or pawn goods. Imagine you just killed a guy who's trying to kill you, and he was carrying a shotgun. Would you sell his shotgun for loot? Where, how? Why do all these merchants in games happily buy whatever bloodstained armour and second hand swords you bring them!?
This is not nessesarily a 'stealth game' as in a stealth game it's often a bit silly like 'if you are seen by anybody at all, everybody comes to attack and you must fight!' Metal Gear being a slight exception because you can run away and hide again, but it's very hard.
I would call this a 'passive action game' or a 'running game'.
If you've ever been somewhere you're not meant to be, and been spotted, most people don't actually attack on sight, and even if they did, there's generally a moment where they're a bit startled by the appearence of somebody who isn't meant to be there. Most people will actually either assume the person probably should be there, or will ask 'hey, what are you doing here?' first. For a while, in Japan, I played 'airsoft' a game where teams hide on woodland or similar environments and try to shoot each other with replica guns that fire plastic pellets. You would be amazed how hard it is to hit somebody running as fast as they can! Even with a machine gun, and especially when there's cover around. Running is a great tactic.
How do we introduce challenge into this game? Well, being caught in the open is very dangerous for a start, and there's still a stealth element, but the challenge if you're seen is not to fight your way out, but it becomes a chase, where you must use your superior mobility to get away to a safe location or hide. Also challenges could spring just from trying to reach areas with acrobatic feats, which would bring in a 'Prince of Persia' element.
Suppose you played an elf like the ones from 'Lord of the Rings', with a cloak that allowed you to blend in with stone or with natural environments (because you'd look like a rock). You have more acrobatic ability than any normal human. Perhaps you must infiltrate a castle to free a princess? Or get around a city, hunting thieves, while the city guard are after you for being an illegal immigrant? This would make a game which would play a bit like Prince of Persia and a bit like Thief/Metal Gear Solid, but with the added element that when something attacks you, your primary tactic is to run away really fast. There could also be an element of the classic 'Sonic' games here, because you'd get the exhilleration from moving fast rather than fighting (attacking anything in Sonic is only useful for points and/or removing the hazard generally). Since you can only hide in certain areas or near certain surfaces (ie. unpainted rock or natural areas) there is a challenge of finding where to hide.
This was rather a long musing session, but I think 'running away' was a concept worth exploring.