K-means finds partitions in a single vector based on any heterogeneity in that vector. It won't automatically find two clusters unless you tell it to find two clusters out of the n possible clusters where n is the finite number of observations in your sample. It's only by generating up to n clusters and then using some sort of decision rule for cluster selection that you could arrive at two clusters.
There are literally dozens of unsupervised classification or clustering algorithms that would work with your example: hierarchical approaches, disjoint solutions, etc., should be at the top of the list. These methods are strewn throughout the literature but good inventories of the many nuances in approaching cluster analysis can be found in the big stat package documentation, e.g., the SPSS or SAS online manuals. That said, there are algorithms that definitely will not work, such as knn or any distance-based, similarity or dissimilarity technique which relies on a p dimensional space to define the solution.
If you have a target enabling a supervised approach, CART would be a good method for partitioning based on a single predictor.