Using SSH The common approach for handling git authentication is to delegate it to SSH. Typically you set your SSH public key in the remote repository (e.g. on GitHub), and then you use that whenever you need to authenticate. You can use a key agent of course, either handled by your desktop environment or manually with ssh-agent and ssh-add.
To avoid having to specify the username, you can configure that in SSH too, in ~/.ssh/config; for example I have
Host git.opendaylight.org User skitt and then I can clone using
git clone ssh://git.opendaylight.org:29418/aaa (note the absence of a username there).
Using gitcredentials If the SSH approach doesn't apply (e.g. you're using a repository accessed over HTTPS), git does have its own way of handling credentials, using gitcredentials (and typically git-credential-store). You specify your username using
git config credential.${remote}.username yourusername and the credential helper using
git config credential.helper store (specify --global if you want to use this setup everywhere).
Then the first time you access a repository, git will ask for your password, and it will be stored (by default in ~/.git-credentials). Subsequent accesses to the repository will use the stored password instead of asking you.