Below is a list of some of the best free APIs for generating charts.
1) Google Chart
The Google Chart API lets you dynamically generate charts. Google chart API is an online service and needs an internet connection. It works by sending an URL to google which will return the chart image. It is very simple to use and if you need abstraction from writing url's you can use any freely available libraries like gchartrb or javagooglechart
The focus is on simple usage (all settings are optional), attractive looks and interactive features like zooming.Although Flot is easy to use, it is also advanced enough to be suitable for Web 2.0 data mining/business intelligence purposes which is its original application.
3) Open Flash Chart
Open Flash Chart is a Flash charting component. It is fairly easy to setup and has classes written in PHP, Perl, Python, Java, Ruby on Rails, and .Net to connect to the Chart. You can create some really nice looking Bar Charts, Pie Charts, Area Charts and etc…
AmCharts is a set of Flash charts for your websites and Web-based products. AmCharts can extract data from simple CSV or XML files, or they can read dynamic data generated with PHP, .NET, Java, Ruby on Rails, Perl, ColdFusion, and many other programming languages.
PlotKit is fully documented and there is a quick tutorial to get you started.
PlotKit is a complete rewrite of CanvasGraph. It is better structured and supported.
PHP/SWF Charts is a simple, yet powerful PHP tool to create attractive web charts and graphs from dynamic data.
You can use PHP scripts to generate or gather the data from databases, then pass it to this tool to generate Flash (swf) charts and graphs. Any other scripting language (ASP, CFML, Perl, etc.) can be used with XML/SWF Charts (the XML version of the same tool.)PHP/SWF Charts makes the best of both the PHP and SWF worlds. PHP scripts provide integration, and Flash provides the best graphic quality.
Visifire is a set of open source data visualization components - powered by Microsoft® Silverlight™. With Visifire you can create and embed visually stunning animated Silverlight Charts within minutes. Visifire is easy to use and independent of the server side technology. It can be used with ASP, ASP.Net, PHP, JSP, ColdFusion, Ruby on Rails or just simple HTML.
FusionCharts Free is a cross-browser and cross-platform flash charting component that can be used to render data-driven & animated charts for your web applications and presentations.
JFreeChart is a free 100% Java chart library that makes it easy for
developers to display professional quality charts in their applications.It has a flexible design that is easy to extend, and targets both server-side and client-side applications. It also supports many output types, including Swing components, image files
(including PNG and JPEG), and vector graphics file formats (including
PDF, EPS and SVG)