WinDbg

WinDbg is a graphical debugger from Microsoft. It is actually just one component of the Debugging Tools for Windows package, which also includes the KD, CDB, and NTSD debuggers. Its claim to fame is debugging memory dumps produced after a crash. It can even debug in kernel mode.

GDB

GDB is the GNU Project's debugger. Security folks use it to analyze unknown binaries, by getting disassemblies and stepping through a program instruction by instruction. GDB can debug programs written in Ada, C, C++, Objective-C, Pascal, and other languages.

Immunity Debugger

Immunity Debugger is a debugger whose design reflects the need to write exploits, analyze malware, and reverse engineer binary files. It builds on a solid user interface with function graphing, the industry's first heap analysis tool built specifically for heap creation, and a large and well supported Python API for easy extensibility.

OllyDbg

OllyDbg is a 32-bit assembler level analyzing debugger for Microsoft Windows. Emphasis on binary code analysis makes it particularly useful in cases where source is unavailable. OllyDbg features an intuitive user interface, advanced code analysis capable of recognizing procedures, loops, API calls, switches, tables, constants and strings, an ability to attach to a running program, and good multi-thread support.

IDA Pro

Disassembly is a big part of security research. It will help you dissect that Microsoft patch to discover the silently fixed bugs they don't tell you about, or more closely examine a server binary to determine why your exploit isn't working. Many debuggers are available, but IDA Pro has become the de-facto standard for the analysis of hostile code and vulnerability research. This interactive, programmable, extensible, multi-processor disassembler has a graphical interface on Windows and console interfaces on Linux and Mac OS X.