Balsamiq is my favorite tool for getting a quick idea into some form of visual representation. I've used it to sketch out everything from mobile app concept ideas to my own portfolio website (aka this one!).

I've found paper prototyping to be the best way for me to get flow issues identified without too much investment. I typically use posterboard and pencil. 

Sketch is my favorite tool all around. I typically use it for any higher-fidelity screen mockups, logo creation, and really any other type of image handling.

To be honest, I hate Invision's interface, but I've used it many times to create app walk-throughs, or run targeted usability tests on a particular task. 

I like Proto.io as a not-too-hard-to-learn tool for high-fidelity interfaces. It's also web-based, which is great for collaboration.

I have used Axure in the past for high-fidelity prototyping with light coding. I'm definitely willing to learn this tool more thoroughly.