The inspiration I am having right now seems to be a very potentially a difficult and challenging topic, but, nothing is else is coming to mind, so here I go.

Blood.  It makes quite a few people very squeamish.  I know I dread getting shots or giving blood, but sometimes it needs to be done.  But blood also was a part of more then a few ancient traditions, and often in different ways.

The most significant and seemingly enduring symbolism of blood is life.  Because when a human being, or an animal is cut or pierced, they bleed and this red fluid comes out, and if enough red fluid comes out, that person or animal dies.  And so, anything that has a red fluid, or could be used to produce a red fluid like substance, became symbolic of this red fluid that seemed to be the vital fluid and liquid of life.  Thus trees that produce red sap, minerals that could produce red pigments, plants that would produce red dyes, and everything else that would produce red. Because of the primal, atavistic recognition of the importance of blood, red is probably one of the three most long lasting and widely used colors, the others being white and black.

Over time, the importance and value of blood and it’s life power became recognized in various cultures.  In ancient burials, people’s bones would be rubbed or dusted with red ochre, perhaps as sign or significance of their blood returning to the earth, or with the thought that they might rise up again, perhaps has a spirit, or being reborn. The word “bless” actually comes from a root word meaning blood, as the method of blessing things in some culture was to sprinkle the blood of sacrificed animals upon them, either items or people.  In modern Northern European paganism, they celebrate “blots” which originally referred to the offerings of blood that were involved in such events.

Because of the  significance of blood, who had control of it’s spilling, and also its source, became very important and controlled especially when it came to humans.  Many ancient cultures probably had laws governing menstrual blood.  While there are still continuining examples today, such as Orthodox Judaism, Islam, and Hinduism, although some of the countries where these religions operate have deemed those laws to be unfair and unequal to women (which they are) some people still follow them out of tradition.  Thus women become set aside during their menstrual period.  I suspect this was widespread through the ancient west, as Agrippa makes note in the 3 books of Occult Philosophy that menstrual blood, and even the shadow of menstruating woman was deemed to be very hazardous and even dangerous to everyone around them, as it might blight crops, stop cows from milking, kill lesser animals, and bring infertility to other women and impotency to men.  A very different viewpoint from most modern paganism, which has been strongly influenced by feminism and the movement to bring justice and equality to women.
The other image of blood, supported by the movie industry, is of course one of human or animal sacrifice, usually portrayed as horrific act involving torture and barbarous methods of butchery for the target involved.  While in most things I have read, it seems less and less likely that ancient mediterranean cultures did practice human sacrifice, there is still documentation of it occuring in other parts of the world, although usually in very special and specific cases.  While in most of the Western World, animal sacrifice is also gone to a certain degree (outside of Kosher and Halal traditions) in Africa, and the african diaspora, Animal sacrifice plays a role, and blood is often the key part of the sacrifice.  As blood is considered the vital essence, it is that which is usually offered to the gods and spirits, whereas the muscle maybe kept and cooked and distributed to the community to eat and feast.  Unlike in horror movies, the sacrifice is usually done respectfully , with very little suffering, and is more like a ritualized method of butchering the animal then the horror movie shocker of torture, mutilation and waste.
An example of offering blood from ancient Sparta  was in a ritual to Artemis.  One of her priestess would hold her image, while men would take a whip and beat the new young men, until the blood flowed freely down their backs.  If the image grew heavy, the priestess would say so, as that was a sign that the man was holding back, as he favored the young man and wished to lessen the harm.  This was a ritual to propitiate Artemis’ wrath for the grave insult that was done to her by the Spartans.  Originally they thought she wanted them to kill one of the young men, but realized that only their blood was needed, so the scourgings began instead.  After being scourged, the young man was officially a man, and no longer a boy or youth.

There is some people who given blood in modern practices.  Some of them are reconstructionists, trying to recreate the pagan past as honestly and correctly as they can. Others might be unallied to any particular group, but following intuition and inspiration, will give their own blood, or perhaps blood collected from butchers.  The easiest way to give your own blood is with diabetic needles, as they are often sold sterilized, and really all you need is just a drop.
Another way you can give blood though is more metaphorical.  The phrase “blood, sweat and tears” as a sign of hard work and effort put into a project would be a fitting offering to the Gods and spirits that you seek a relationship with.  This “blood” is often just as acceptable, or even more so then physical blood in this day age.