As Tarek said, Amber Diceless is a strong rpg. Other rpgs are where the narrative is controlled by the players and not the GM. There games as such that are listed on the website over The Forge (sorry don't know the link, but I think some of the other posters can help here).
Also, if you want to avoid the "kill things and take their stuff" type of rpgs, you'll need to play games where that is not factored into the design at all or actually maybe considered to work against the players for doing such actions. Of course, the only fantasy games I play are these, but I know that there are a ton of other fantasy games where this is heavily discouraged.
Now, if you still want to play D&D, you'll have to houserule the mechanics that provide reward.
For example, you identified two elements about the game that you didn't like 1) getting treasure and 2) killing enemies. First off, remove all the reward conditions for doing so. For example, you don't reward player characters for killing (or even defeating their enemies). You also have to remove the implied rewards too (kill everything, beat the adventure). So in this case, you'll need to design your adventures where wasting everything actually does more harm than good. For example, killing the thugs that kidnapped the princess, the PC's find out they buried her alive and now that they are dead, well, oooopsss....
For the second thing, getting treasure. This is harder, because D&D is built that the balance of power for characters is also through the amount of equipment they possess, so the mechanics of collecting the +5 sword, +4 belt of strength, +2 ring of protection, etc. is part of the game or else fighting that dragon at the party's CR is not only difficult, but probably impossible. You'll have to devise mechanics that supplements these bonuses either through feats, stackable spells, talents, or some other abilities so that you can do away with having to reward the players this (assuming of course, you want them to be able to fight such monsters to begin with). Lastly, there is the thing about that if you don't even want the player characters to be chasing after gold pieces, then you'll need to change the economy to more of a bartering system and have any kind of coinage quite rare. Or you can use some resource mechanic in which to acquire goods and services is a DC against a player character's wealth score / skill / feat / etc.
The next thing is to get your players on board with the change of the mechanics. If your players support this, they will go for it; otherwise, if you try to hammer it into their heads, they are likely to rebel given their expectations of the game versus your expectations. For example, if the goal of your players is to just kill things and take their stuff, you're going to have an incredibly hard time to drive that point across even after altering the mechanics of reward.
For me, this or any similar approach wouldn't work with my players. They love the whole trope of blasting every baddie they come across and looting their smoldering corpse. I think I fall within this camp as a player too, but I could see myself playing in this kind of campaign too if the occasion arose.
Anyways, good luck on finding your game or making the changes to your current game!
