Tools help to get stuff done.

Programming

• Text Editors
• Notepad++ - a lightweight all-purpose editor
• Hex Editor Plugin - a Notepad++ plugin
• IDEs
• Visual Studio 2013 - C++, .NET (VB, C#)
• Visual Studio Express - a free version of the above
• Eclipse - a popular Java IDE
• Code::Blocks - C++ (used by Red Eclipse)

Flash Reverse Engineering

• Bytecode Editors
• Flasm - edit AS2 bytecode
• RABCDAsm - edit AS3 bytecode (can even edit multinames)
• Yogda - edit AS3 bytecode, but good for searching strings and identifying DoABC blocks to edit
• Decompilers
• JPEXS Free Flash Decompiler (ffdec, googlecode/asdec) - see deobfuscated AS2/AS3 ActionScript beside bytecodes, can edit
• Sothink SWF Decompiler - view recompiled AS2/AS3 ActionScript, can reassemble .fla and show thumbnails of sprites
• SWFWire Inspector - view recompiled AS2/AS3 ActionScript
• Miscellaneous Tools
• SWiX - Edit some tags (like shapes and text) as XML
• SWFiD - Detect some packers/crypters and dump from memory

Remote

• FileZilla - an FTP/SFTP client
• Putty - an SSH client
• RealVNC Viewer - a VNC client

* Free software is good.
** Free and open-source software is even better.