Note: there are dozens of platform and device specific apps for note taking and project management. My criteria are that the program needs to be budget friendly and work no matter which device I'm using.
Evernote - no option for Linux, but it works on most phones
Zim - this one might be a little geekie for some people, but I like it because I can keep it in Dropbox and use with pretty much any OS
Trello - this doesn't offer offline access, but even the free version has a ton of tools for collaboration and project management
XMind - I've used a lot of mind mapping programs, but I chose XMind because the free version XMind has tons of features and they have versions for almost every operating system
Project Libre - a free, open source desktop alternative to MS Project
Glip - an online project management/collaboration platform
Premium Project Management with Free Options
These three premium platforms offer a free tier, but they tend to limit the number of projects or lack some of the more useful features like dependencies, instant messaging, and video chat that are available in the paid version.