D3 – is really amazing and I love it’s simplicity. The documentation is really extensive, the source code is hosted on GitHub, and the examples are never-ending. There is a D3 prototyping tool called Tributary with many great examples. It’s so good that xcharts, nvd3, Rickshaw, Cubism.js, dc.js, and xkcd are all based on D3. If you are making some amazing custom data visualizations, D3 should probably be your choice, otherwise these d3-based libraries mentioned above are great for more simple straightforward graphs. Finally, I highly recommend looking at Scott Murray free book on D3 called Interactive Data Visualization for the Web and Dashing D3 tutorials.
HighCharts – very powerful, I love the JSFiddle examples and powerful features. I don’t like the license fee but they have great customers (IBM, NASA, MasterCard, etc). They also have backward compatibility with IE8.
jqPlot – if you are already using jQuery, you don’t want to pay for HighCharts, and D3 is too much for your simple use cases, then jqPlot is an excellent choice.
Google Chart Tools – powerful, free, simple to use, and it has everything from simple line charts to complex hierarchical tree maps, the chart galley provides a large number of well-designed chart types.
xcharts – a D3-based library for building custom charts and graphs.
nvd3 – allows you to build re-usable charts and chart components without taking away the power that d3.js gives you.
Cubism.js – a D3 plugin for visualizing time series. Use Cubism to construct better realtime dashboards, pulling data from Graphite, Cube and other sources.
jQuery Sparklines – a jQuery plugin that creates small inline charts directly in the browser.
peity – a simple jQuery plugin that converts an element’s content into a simple CANVAS mini pie, line or bar chart.
BonsaiJS – lightweight graphics library with an intuitive graphics API and an SVG renderer.
jQuery-Visualize – HTML5 canvas charts driven by HTML table elements. Another charting plugin for jQuery.
moochart – is another plugin for MooTools and it focuses on drawing bubble diagrams on the canvas tag.
table2chart – a MooTools plugin that generates charts from accessible data tables.
Canvas 3D Graph – a special type of bar graph that plot numbers in 3D.
ArborJS – a graph visualization library using web workers and jQuery.
TimePlot – focused entirely on graphing time-series data, with support for annotating the graph with temporal events.
gRaphael – create stunning charts on your website, based on Raphael graphics library.
ZingChart – allows you to build advanced charts and visualizations in HTML5, SVG, VML and Flash.
RGraph – produces interactive charts using the HTML5 canvas tag.
Dojo Charting – if you are already using Dojo, then Dojo’s charting library is a great solution for making charts and graphs.
JSXGraph – a cross-browser library for interactive geometry, function plotting, charting, and data visualization in a web browser.
jGraph – HTML5 diagramming component with full IE 6-8 and touch device support.
Sencha Touch Charts – it uses HTML5 Canvas and CSS3 to deliver charts to the mobile web browsers.
Style Chart – a free Ajax Visualization Charting Service
If you are looking for more libraries and web services that deal with visualizing data, I recommend checking out Datavisualization.ch.
Graphene – a realtime dashboard & graphing toolkit based on D3 and Backbone.
jQuery ToastChart – a line-graph charting library that is designed to show all types of data using the HTML5 canvas element.
ChartsJS – Easy, object oriented client side graphs for designers and developers.
Ember Timetree – visualize hierarchical timeline data with Ember.js and D3.js.