Specifically, I maintain a git repository of my dotfiles. I recently started working on a new machine and cloned my repository on the same.
Now, I wish to make some changes to my dotfiles which are specific to this system only. These changes I wish to ignore in my repository.
Other changes that I make, should continue to be tracked and committed.
For example, in my .gitconfig, I have a setting as:
default = simple
git update-index --assume-unchanged
I don't believe there's a specific command that will 'untrack' certain changes to a file. However, there's no reason that you couldn't create a local branch into which you pull changes from your remotes, but never send any changes back.