If a repository has no license, then all rights are reserved and it is not Open Source or Free. You cannot modify or redistribute this code without explicit permission from the copyright holder.
I'm unsure of the legal implications of actually pulling the source local and building/using the software privately though. Perhaps someone else can chime in on that.
You're under no obligation to choose a license. However, without a license, the default copyright laws apply, meaning that you retain all rights to your source code and no one may reproduce, distribute, or create derivative works from your work. If you're creating an open source project, we strongly encourage you to include an open source license. The Open Source Guide provides additional guidance on choosing the correct license for your project.
Note: If you publish your source code in a public repository on GitHub, according to the Terms of Service, other GitHub users have the right to view and fork your repository within the GitHub site. If you have already created a public repository and no longer want users to have access to it, you can make your repository private. When you convert a public repository to a private repository, existing forks or local copies created by other users will still exist.
In short, the only thing you can safely assume is that you have no rights to do anything at all with this code. In the particular case of GitHub, you can fork the repository and view the code, but nothing more.
DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
Version 2, December 2004
Copyright (C) 2004 Sam Hocevar <sam@hocevar.net>
Everyone is permitted to copy and distribute verbatim or modified
copies of this license document, and changing it is allowed as long
as the name is changed.
DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
0. You just DO WHAT THE FUCK YOU WANT TO.
Hey, would you mind choosing a license for your project, if it's meant to be open source?
What can I assume if a publicly published project has no license?
My personal favorite is the WTFPL: