Sometimes I see some answers which are really good and I'd like to save. Similar to how we follow questions I'd like to have the ability to 'save' answers implemented in this site
You can't bookmark an answer, but you can follow it. This is a new feature which isn't completed yet; at the moment, there's no list of followed posts in your profile, but this will be implemented soon.
One of the downsides may be that you receive notifications about edits and comments on that answer; for a full list of differences, see this proposed FAQ.
A temporary workaround might to use the bookmark system of your browser.