n-dimensional searching alogrithm

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If you want to store various points in a $n$ dimensional (here $n=2$) space. Is there a possibility to do that with a tree (as a binary-tree for $n=1$ is usually used) for efficient and fast finding nearest points to given coordinate?

Does someone know how these technique or algorithm is called?

In other words: I want to find the nearest point $\vec r_\text{nrst}=(x_\text{nrst},y_\text{nrst})$ in a set of points $r=\{\vec r_1, \vec r_2,...,\vec r_k\}$ to a given point $\vec r = (x,y)$. And all this very fast for big values of $k$.

[Edit:] Now I am using an own implementation of a quadtree to do the storage.