This is a good question - It was hard to think of in those terms.
But I think this is a good 'all programmer' type of question.
I can only speak from my personal experience, but the short-answer is: there are many, non-programming tools, in different contexts.. too many to list.
Structure, Requirements, and Design.
What non-programming tools do we use?
Some short, subjective aspects I see are:
methodology tools, learning tools, delivery and maintenance tools, structure tools, design tools... So, here we go.
We reuse a significant amount of methodology and best-practice to build structure, define requirements, and conduct creative-design.
There are two non-programming disciplines that are remarkable, UML modeling language, and Agile Development Methodology. These have much to do with Structure, Requirements and Design.
But there is more...
StackExchange is a gold-standard non-programming tool that give you the ability to program. Word up Stack-x. Then there is GitHub, don't even know where to start with that one. To me, GitHub is da bomb. Use GitHub as a social-coding tool to learn-by-doing. And with technologies unfolding on a week to week rate, Twitter, is a powerful learning tool to keep up with rapidly emerging events. Blog, Wordpress, it is important.
there is more..
REQUIREMENT - DELIVERY & MAINTAINING:
Probably, there are more encompassing tools of delivery than actual IDE's (Integrated Development Environments), in most of programming. We use a lot of add-on software... without really any second thought of it. There are a number of procedural tools to fulfill requirements. I'll keep it short, All Repositories, Merging, and Collaboration tools. So, GitHub again. Continuous Integration, Automation tools, Testing tools, FTP. Building tools tasks and add-ons, Compressing. Then there are services, browser-extensions, plugins, it is vast, sir. Something to be admired perhaps.
Pair Programming. Whiteboard. Get a WhiteBoard. Someone mentioned paper and pencil. So true! This is specifically used for user interfaces and increasingly for things like Mobile Design. There is also a massively, silently growing awesomeness over at Google, in Chrome Developer Tools. DevTools and FireBug is pretty much Non-Programming (for the moment - kind of). They are advancing rapidly toword providing activities like: Design - In the browser... So, structure on the fly, in-design, instant match to requirements style.
Code can be structured in a very large number of ways.
One very important area of mention is: Design Patterns.
They result in about a hundred ways to do things like MVC, which stands for Model-View-Controller. So we have framework tools that provide Structure. There are so many it is exasperating For example, producing any number of Diagrams, Documentation, Direction, screenshots, videos, printers. Google Docs gets an honorable mention here, then there is a myriad of others like dropbox.
FRAMEWORKS as a Medium:
These type of frameworks extend a best-practice of a technology. They are essentially tools to build on. It is hard to not mention: Backbone.js, Node.js, or three.js, micro-libraries, jQuery, ExtJS. Stuff like that...
MORE NON-PROGRAMMING DESIGN-TOOLS:
UX : User-Experience is increasing in importance.
A relatively new Front-End discipline is RWD - Responsive Web Design. Knowing these best-practices are mental tools to drive requirements like multi-device adaptivity. Which embodies evolving best-practices of structure and design.
Take a look
I hope that helps (with minimal typos).
All the best!