While the carbon backbone common to most organic molecules makes isomerism common in these compounds, inorganic molecules can also exhibit isomerism or chirality.
A common example of a nonorganic molecule which exhibits isomerism is cisplatin (also know as cisplatinum). This molecule, H6Cl2N2Pt, is used as a chemotherapy drug. You can view diagrams of the isomers of cisplatin at this link. Cobalt III is another atom that is capable of forming different isomers.
Another example of non-hydrocarbon isomerism is found in examining very large biological molecules such as proteins, where different patterns of folding result in a form of functional isomerism.
Isomers are compounds that have the same molecular formula, but can have more than one structural formulas. This means that while the ratio of atoms, of different elements, remains the same the layout of the atoms differs.
Hydrocarbons only consist of hydrogen and carbon atoms, and isomers do exist among hydrocarbons. But, when you substitute at least one of the hydrogens with another element, or a functional group, the isomers still exist. Once this substitution occurs, the compound is no longer a hydrocarbon.
For example, CCl2F2 is not a hydrocarbon but does have more than one possible structure.