Network analysis

DNA, for discourse analysis

Graph Commons: simple and beautiful interface for collaborative network-building, with some basic network algorithms built in - you can also import/export data; check it out.

gephi: very popular tool for network science. Gephi tutorials

NodeXL another popular tool that works in conjunction with Excel (mainly Windows - but there are solutions for mac too)

Ucinet: one of the standard SNA packages, along with Pajek.

SocNetV: easy to use, but a bit buggy last I checked. Will run a "spider" mapping a portion of the web.

NetworkX: a Python package for network analysis (requires programming)

Network Analysis and Visualization with R and igraph (requires programming). Another R package is here

igraph or igraph, an open source C (programming language) library for the analysis of large-scale complex networks, with interfaces to R (programming language), Python and Ruby

Tools at Carnegie Mellon's Center for Computational Analysis of Social and Organizational Systems (CASOS)

ORA, a tool for Dynamic Network Analysis and network visualization. Kathleen M. Carley, 2014, ORA: A Toolkit for Dynamic Network Analysis and Visualization, In Reda Alhajj and Jon Rokne (Eds.) Encyclopedia of Social Network Analysis and Mining, Springer.

Orange, a free data mining software suite, module orngNetwork

Meerkat: developed by our own CS folks; runs in Java

Tulip, a free data mining and visualization software dedicated to the analysis and visualization of relational data. [1]

SEMOSS, an RDF-based open source context-aware analytics tool written in Java, leveraging the SPARQL

webweb, to display interactive networks in a browser.

And many others...