1) Balsamiq mockups for wireframes
Quickly mocking up a UI for brainstorming sessions is a very useful thing. When you're doing the first pass of what a new screen will look like, you usually don't need photoshop-quality finish - Just a quick way to layout your screen so you can see if all the elements work together. Balsamiq mockups is the tool for this job. It lets you quickly mock up web, desktop or mobile screens, and drag-drop UI elements to create easy-to-understand wireframes. Great for quickly brainstorming ideas over new features!
Balsamiq Mockups - http://www.balsamiq.com/products/mockups
2) Quick diagrams with Lucid Charts
Every so often, you need to create charts and diagrams to capture a high-level idea. It could be anything from your software architecture to your projected org chart. Quickly putting together such charts used to mean firing up PowerPoint and using the diagramming tools in PowerPoint to create simple charts and diagrams. LucidCharts provides an easy and quick to use alternative that lets you get started quickly and build professional looking diagrams on the cheap. Lucid Charts can scale to really big diagrams as well - You could probably draw out your whole software architecture in UML if you wanted to (but why would you want to do that?) In any case, Lucid Charts is a great tool to try out.
Lucid Charts - https://www.lucidchart.com/
3) Mouseflow for website heatmaps
Mouseflow is one of the coolest tools in this list. Basically, it lets you see how your users interact with your web application and generate analytics that can help you decide how to approach new features, what parts of the site are getting used more (or less). One of the most interesting things that Mouseflow can do is to create a "heatmap" of your site - A color coded overlay on your webpage that shows where the user's attention and mouse movements are focused, so you know if your menu is better places on the left side or on the top, for example.
If you have a rich web app, Mouseflow can show you some very interesting insights about how your users are using and interacting with your App.
MouseFlow - http://mouseflow.com/
4) Abstract idea management with FreeMind
FreeMind is what they call "Mind Mapping" software. It lets you capture abstract ideas in a hierarchical and connected set of nodes. If you are not familiar with mind-mapping software, you should give this a try. Abstract ideas are notoriously difficult to write down on pen-and-paper or in any other linear format. What FreeMind lets you do is to let you jot down ideas as the form, and expand on any branch of ideas that seems interesting, and come back and navigate through the various different options that you skipped over earlier.
FreeMind - http://freemind.en.softonic.com/
5) Agile management with versionone
There are many project management tools out there, ranging from the humble spreadsheet to complex tools like Rally and BaseCamp. Versionone is a mid-level tool (that most importantly comes with a free edition). Versionone lets you manage your product development and roadmap using well understood agile methodologies, and lets you get some visibility into when your engineering team is going to finish that feature or bug fix that a customer is waiting for. Versionone is very easy to use and get started with, and will add a level of discipline and trackability to your product development without too much overhead.
Versionone - http://www.versionone.com/