Molecular Biology

Ape - A Plasmid Editor - excellent plasmid editor and sequence analysis tool developed by Wayne Davis at Univ. of Utah. It opens DNA Strider (for all you Mac users), GenBank and other standard formats. Runs on Windows and Linux
4Peaks - software for viewing and editing sequence trace files from the guys who made 'Papers' (Mekentosj). For Macs only
EnzymeX - sequence analysis and editor (Mekentosj). For Macs only

Chemistry

PubChem - free database of chemical structures from NCBI
PyMOL - 3D structure viewer for proteins
ACD/ChemSketch - tools for drawing and viewing 2D/3D structures
Marvin/JChem - cheminformatics tools for managing and analyzing chemical structures

Synthetic Biology

Clotho - design tool developed at UC Berkeley
GenoCAD - tool to build genetic constructs developed at Virginia Tech
BioBricks - database of synthetic parts to design devices and systems

Data Analysis and Visualization

Cytoscape - an Open Source Platform for Complex-Network Analysis and Visualization
Cell Profiler - cell image analysis package from The Broad Institute
R - free software environment for statistical computing and graphics
Google Visualization - free tools to generate web based charts and graphs