In the past decade, parameterized unit testing has emerged as a promising method to specify program behaviors under test in the form of unit tests. Developers can write parameterized unit tests (PUTs), unit-test methods with parameters, in contrast to conventional unit tests, without parameters. The use of PUTs can enable powerful test generation tools such as Pex to have strong test oracles to check against, beyond just uncaught runtime exceptions. In addition, PUTs have been popularly supported by various unit testing frameworks for .NET and the JUnit framework for Java. However, there exists no study to offer insights on how PUTs are written by developers in either proprietary or open source development practices, posing barriers for various stakeholders to bring PUTs to widely adopted practices in software industry. To fill this gap, we first present categorization results of the Microsoft MSDN Pex Forum posts (contributed primarily by industrial practitioners) related to PUTs. We then use the categorization results to guide the design of the first characteristic study of PUTs in .NET open source projects. We study hundreds of PUTs that open source developers wrote for these open source projects. Our study findings provide valuable insights for various stakeholders such as current or prospective PUT writers (e.g., developers), PUT framework designers, test-generation tool vendors, testing researchers, and testing educators.