Data about many different topics and from various sources can be gathered through (open) APIs. You will find them on the websites of many companies delivering SaaS or you can check them out on one of the sites that offers aggregated lists of almost all available APIs.

On https://www.programmableweb.com/ or http://mashable.com/, you will find many APIs that you can use for inspiration. You will also find many mash-up solutions there. You can find many APIs that you can use for your app. Most of them are not explicitly intended for mobile apps but as long as the data can be consumed as JSON or as XML then that does not really have to be an issue. On the website, you can search for particular categories, particular data types, or just browse through the latest additions. As you can see, following the weather is always an interesting kind of data source and there are...