If you have the Enterprise version of SharePoint you may use the Excel Access Web Part to display charts on your pages. If you don’t have Enterprise license, but have Office Web Apps installed, you can use Excel REST. This should work both for SharePoint 2010, SharePoint 2013 and SharePoint On-line.
Research led me to creating a web part, much similar to the Excel Access Web Part, but also a bit improved. My next thought was to create this as an SharePoint App, but due to several factors of the App model, that project is now on ice and cannot be completed due to the lack of API’s.
Long story short, I’ve taken the code I have and made it into a sandboxed solution located at https://spexcelchart.codeplex.com/. It’s tested with 2013 on-premises and SPO, but should be easy to compile it for 2010 if you want.