Today, governments, organizations, and corporations around the world are beginning to participate in the open data movement. Terabytes upon terabytes of open data are available and ready to be mashed up into useful applications by creative individuals like YOU. We would explore the various datasets that are most commonly used, however you can freely explore other open source datasets.
Data.gov is a repository for federal government information, made available to the public. All of the data is available in machine readable form, so you can easily retrieve data from data.gov using javascript. Data.gov has datasets related to all aspects of government like consumer complaints, international trade, zip-code, hotels, restaurants, etc. You can search your dataset of interest here.
Open Indy Data Portal is similar to data.gov, but Open Indy focuses on the City of Indianapolis. The OpenIndy Data Portal contains all data required by Disclose Indy, a plan to promote honesty, integrity, and cost savings in local government. It provides public access to the following information: city or county contracts, ethics filings, campaign finance reports, crime statistics, community resources, budget and spending information, audits, etc.
Climate Data Online provides statistical data related to various aspects of climate and weather like precipitation, temperature, rainfall and so on. The data is available for various levels of granularity - hourly, daily, monthly. You can read about the API here.