I'd like to implement procedural world generation, but I don't want it to look gridded or blocky, where everything is obviously placed on an integer grid.

I know that you can do this in gridded worlds by inputting a square's x and y into a noise function, or similar, but is it possible to generate a more natural looking object placement using procedural methods?

This is in the context of an adventure game, if it matters.

Edit: I guess I should have been a bit more clear in my original question, but I'm mostly wondering about the actual placement of objects in game, e.g. trees, buildings.