There are many software options available for professional web designers / developers. The software can be broken down into different categories, but ultimately depends on the website solution or application being designed / developed.
Administrative / Planning
Microsoft Word is great for creating sitemaps and notes for your web projects.
Photoshop is the most widely used program for creating wireframes and designing websites. While there are other options available for creating your design layouts for a website Photoshop tops them all.
Illustrator is used by professional designers to create graphics / illustrations for web projects.
Notepad++ is a lightweight text editor for Windows which has extension support for developers. While great for hand programming small static website it lacks in features for advanced programming.
Sublime Text is a sophisticated text editor with many more features than Notepad++. A great program for hand coding small and large website, and available for Windows, Linux and OS X.
Testing / Debugging
Browserstack web based software used for cross-browser testing. There is a monthly fee for the service, but very much worth the cost for developing cross-browser friendly websites.
The software you ultimately choose or may need depends on the type of website being programmed. This post primarily focuses on web design and frontend programming software. There are many more software options and needs for developers depending on the complexity and architecture of the program.