libSBML

LibSBML is a free, open-source programming library to help you read, write, manipulate, translate, and validate SBML files and data streams.

It's not an application itself (though it does come with example programs), but rather a library you embed in your own applications. The program offers powerful features such as reading/writing compressed SBML files, detecting overconstrained models, checking units, an API for SBML content, and support for the three most popular XML parser libraries: Xerces, Expat, and libxml2.