SAGE Research Methods provides datasets intended to teach how to clean and analyze data using common software such as Stata, SPSS, R, and Python. Datasets are ready to use, formatted for the software of choice, and come with codebooks, documentation, and how-to guides.
ICPSR also provides guides and exercises to walk through the process of analyzing datasets, with pre-cleaned data.
Check out these examples:
Replicating previous research increases the rigor and quality of future research. It is also a great way to practice and develop data analysis skills.