One way to find tools suited to your task is to browse galleries of innovative visualizations such as Visual Complexity and Infosthetics.
Google Maps: This classic solution adds spice to any geographic data.
modest maps: an open source Flash mapping solution that works with most major mapping backends.
Open Layers: An open-source Google Maps clone.
Mapstraction: An abstraction layer for different JS mapping tools including Google Maps, OpenLayers/OpenStreetMap, poly9 FreeEarth, and more.
R and ggplot2
SOCR Tools: Web-based applets, computational libraries, educational and data resources
Matplotlib: Python 2D plotting library. Useful for generating all sorts of graphs/plots/charts. Highly recommended.
pygooglechart: is a complete Python wrapper for the Google Chart API.
Chart Chooser recommends chart formats based on the type of thing you're trying to show.
SOCR_Charts: The largest openly web-accessible collection of tools for Exploratory Data Analysis (EDA)
Excel Chart Cleaner removes chartjunk from Excel spreadsheets.
Simile Timeline: Great for visualizing time-based data.
many eyes: While they require you to upload your data to them, this site makes getting some good visualizations off the ground quite fast.
Swivel: Another site to upload your data and generate some basic graphs.
Most graph tools seem to concentrate on making cluster-tree graphs, using some form of ball-and-spring model.
Circos is notable for its innovative and beautiful ring-graph visualizations.
Graphviz: Graphviz layout programs take descriptions of graphs in a simple text language, and make diagrams in several useful formats such as images and SVG for web pages, Postscript for inclusion in PDF or other documents; or display in an interactive graph browser. (Graphviz also supports GXL, an XML dialect.)
These tools will scale efficiently for massive graphs that call for parallel processing across computer clusters:
These are typically written in Flash or Java and typically let you explore small local slices from a much larger remote graph.
The Prefuse Gallery shows several beautiful-looking graph visualizations that appear to scale to ~1000s of nodes.
SpringGraph - a simple but clean Flash (Flex) spring graph tool.
Eye-Sys: Windows visualization app launched in late 2007; offers a building-block approach for creating a huge variety of visualization systems. Version 2.0 released in Sept. 2008 includes a suite of graph theory objects, enabling faster and more customizable graphing in 2D & 3D
Processing: This classic workhorse will let you browse through linked RDF data from the comfort of your browser. While I admit most of its examples seem overly artsy, Processing can genuinely be used on real data sets -- indeed, there's a whole book on it.
nodebox: A Mac OS X application, similar to Processing, but using Python as a basis.
prefuse: A visualization toolkit for the Java programming language.
prefuse flare: provides much of the same functionality for Actionscript 3.
Google Visualization API: Embed visualizations directly into your website: Display attractive data on your website by choosing from a vast array of visualizations created by the developer community.theinfo.org