In answer to your question, it depends on what kind of familiar you are talking about. There are physical familiars (living & breathing) and there are the astral type as well. Normally when someone talks about familiars, they are meaning a physical familiar-- one that lends it's strength and attributes to your magickal workings. But the astral familiars are also very valueable.
The astral familiar is more or less any number of creatures that come to you during a meditation and/or when seeking them, which obtains certain characteristics that are necessary to you in your task, be it magickal or just at this time in your life. There are many articles about this subject that detail the best way to find your spiritual/astral familiar, if you were interested in pursuing it further.
So far as the physical familiar, that could be any animal or even bug, pest, etc. that has come into your life. Most common though, are household pets. The best way to test your pet for the familiar characteristics is to open up your magickal space to him/her and see if there is any interest displayed by your furry friend. (Or shelled, or slimy... as the case may be.) If there is interest and even intervention in your magick, then your pet may be acting as your physical familiar. That is a bond that can be worked on slowly and carefully, so he/she can find the best way to offer his/her help to you in your magick, and you can learn the best way to harness and respect what your friend has to offer. Remember, though, that a familiar usually finds us, when we least expect it. It is hard to say when or where we might find our familiar, when we do, they deserve the utmost respect and kindness. In some cases, your familiar will come to you without you even knowing it, or even casting a spell. This is because familiars are spiritual creatures that know to seek us out. If you have an animal hanging around your home that just won't leave, this may be your familiar (as you said about the snake).