As written, I tend to read that a Proficiency can be selected more than once. Some descriptions explicitly state the benefit to doing so, others do not (Healing vs. Caving for example).
If it is not stated, can a Proficiency be taken more than once? I'm particularly thinking Familar here
By core I think only proficiencies that mention some improvement for taking the same proficiency more than once can be taken again.
In many cases proficiencies are a you have the training or you dont without any granularity beyond that.
That said, it is entirely up to your judge if they want to allow it otherwise.
I believe Loswaith is correct, but each campaign is its own. If I recall correctly Tracking doesn't mention in its entry that it can be taken multiple times, but I allow it in my campaign. As for Familiar, while the PC can take it once you might want to take care with how the rules as written would work, since a familiar has access to its master's proficiency list and could take a familiar itself. A familiar chain could be created and before you know it there are an infinite number of familiars in the world. Obviously that's broken, but you might allow a familiar to take the Familiar proficiency whenever the PC gains a new class proficiency slot. The elf in my group at 4th level now has a 2 familiar chain, and it really hasn't broken anything yet.
By default, a proficiency cannot be selected multiple times unless the proficiency description says that it can be.
I think the Familiar chain discussion is on here as well - some good points in it, but overall doesn't appear broken