Tollhouse:
Actually, according to the Midrashic interpretations, the reason he grabbed Esau’s heel was so that he could be born at all. Supposedly, Esau hated Jacob in utero, and attempted to damage his mother’s womb after he emerged in order that Jacob couldn’t come out, but Jacob grabbed his heel so he couldn’t be sealed inside should Esau do such a thing.
In Jewish inheritance law, the firstborn receives twice as much of the estate as his younger brothers. For example, if a man has four sons, the firstborn receives 40% of the estate, and the other three get 20% each. This comes directly from the Bible.
In synagogue ritual, before the Priestly Blessing on holidays (and in Israel, every day), a Levite will wash the Priests’ hands. If there is no Levite in the congregation, then a firstborn gets that privilege instead.
Also, on the day before Passover, firstborns are expected to fast, although this fast is considered a less binding custom than other fasts on the Jewish calendar, and it has become traditional to circumvent by attending a celebration of religious significance (such as the completion of a certain unit of Torah learning) at which food is served.
In Jewish law, the male firstborn of a cow, sheep or goat must be offered on the altar in Jerusalem if in perfect condition or given to a Priest if its body is blemished (in modern times, when the laws requiring ritual purity cannot be practiced, these firstborn animals are left untouched to live out their lives and die of natural causes). Using them for work or shearing them for their wool is forbidden. A male firstborn donkey is also holy, and it can be redeemed giving a Priest a sheep or goat as an exchange for it. And firstborn male people must be redeemed by giving five silver coins to a Priest.
First fruits of trees are also considered holy.
It’s considered the most special because the first product of one’s efforts gives the producer a special sense of satisfaction that is not matched by subsequent iterations. It is therefore considered especially praiseworthy to overcome the sense of personal accomplishment of that occasion and instead acknowledge G-d’s hands in the success of the endeavor.
I think a lot of this attitude extends to present day society, even if as far as human beings go, attitudes have become more meritocratic. Many business owners will frame the first dollar they made, for example.