Homebrew is a useful tool to install UNIX tools.
What are useful things to do with homebrew? What tools can you recommend?
It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.
HomeBrew is a package manager for mac. It facilitates the installation of different tools by installing and configuring all dependencies as well as the program itself.
You can think of it like the Mac App Store for unix apps. If you are familiar with Linux, then Homebrew is exactly like the Linux package manager. For a complete list of everything you can install go here : https://github.com/mxcl/homebrew/tree/master/Library/Formula/
If you don't know what you would need it for, then you probably don't really need it.