I have used a drop or two of my own blood in doing magic.
I used some to empower a set of runes that I crafted. This, from what I have read, was traditional in Northern practices.
In addition, my patron Goddess is Sekhmet. In historical practice, blood was a traditional offering to this Goddess. When I asked her assistance in a healing ritual when my mother had open-heart surgery, I included an offering of several drops of my own blood to her.
Blood carries a bit of your personal life-force. So a drop of blood in a magical working is a sacrifice on your part of part of that life-force. This can be a very powerful adjunct to your magic.
For me, personally, I would not use blood from an animal or another person in my workings. The important thing in my magic is that my blood is a sort of sacrifice to the Gods that helps empower that magic.
Other paths are not so strict. For instance, in some of the African diasporic religions such as Santeria, animal sacrifice is a normal part of their rituals.