This is not software that generates board games, but rather software that helps me in that endeavor. Many of the tools work on my iPhone so I can use them wherever and idea may appear.
Captio – runs on my iPhone and sits in my button home row, when I tap it, an editor appears where I can type or add a photo, when I hit send it sends the text and/or photo to a configurable email address. I have mine go to my inbox, my Evernote, and to my Omnifocus todo manager. link
Evernote – When I find an interesting web page or blog post, or any tidbit of information that I might use later, I stuff it into Evernote. You can also take a photo of a whiteboard where you’ve been working, and it can OCR the information into searchable text. I use the app on my MacBookPro, iPad, iPhone, and via the web. link
Mind Meister – Online collaborative mind mapping tool is great for just dumping ideas for a project and getting them organized. It’s amazing how one idea can lead to another when using this tool. This is a web based tool. link
Photoshop – Card mockups, etc. link
BoardGameGeek.com – Although not technically software, it is an invaluable tool for all things board game related. link