Although there applications and devices available that can track down a mobile phone using GPS, these are predominantly designed with finding your phone if it has been lost or stolen, rather than keeping tabs on a person.
There are ways to track someone using their cell phone number, but to do this legally the other party must give their consent, you cannot track someone without them knowing, and really, you probably shouldn't, either. Their are a lot of ethical and privacy implications of doing this.
Life360 is a website which allow you to register phone numbers to track, and is aimed at families, so parents can ensure their children are safe, and friends can stay connected.
Location tracking apps are very common and rising in popularity, but all have an "opt in" feature where the user agrees to share their location.