(This is a response from H.W. from NYC to my broadcast, "What tribe are you from?")

My father was an Israelite (family stories say we are from the tribe of Judah) and my mother was a Cohan.  Her marriage would be considered a morganic marriage since my father was not a Cohan.

 First of all, Cohanim (plural), are direct descendants of Aaron (Moses’ brother) through his son Aleazar, which was part of the tribe of Levi.  A person's tribe is inherited from the father's side.  While Levites, were the servant of the "LORD", they assisted in the "TEMPLE", the Cohanim, were the priests (they were direct descendants of Aaron). The high priest was called the Cohan a Gordol and the High Priest came from a specific clan/family and it was hereditary.  The eldest son of the High Priest was designated as the next High Priest. 

Even if you were a Cohan, you could not serve as a priest if you:

(1) had any physical or mental defects (i.e. blind, malformation of any body part or missing a limb or speech impediment)and

2) All Cohanim serving as priest must be a child of a mother and father who are both Cohanim. (If a Cohan male married a female who was not a Cohan, it was considered a morganic marriage.

If a male Cohan was not around, a female Cohan who was not married to a non Cohan could perform certain priestly functions.  Both male and unmarried or widowed female Cohanim and male Levite received "Levite's Tithe" (ever family had to give 10% of their income).  If a female Cohan was in a morganic marriage she could not receive the Levite Tithe for income, but once she either divorced or became a widow, the Tithe would continue unless she had another morganic marriage.  Male Cohanim who were in a morganic marriage could not serve as a priest in any capacity unless he became a widower or divorced his wife.  Once that happened his Tithe would be restored as well as his priestly functions, unless he was in another morganic marriage or he was considered unclean due to a physical/mental imperfection.

Cohanim were/are considered inherently holy and the High Priest usually came from one family/clan and it was hereditary.  (i.e the Maccabees, [the Hasmoneans dynasty] who were not only High Priests but Kings of Israel (140–37 BCE).

It is also believed that many families who were part of the Northern Kingdom migrated to the Kingdom of Judeah (in the south), when they felt they were about to be attacked by the Assyrians.  Thus the Kingdom of Judeah was not only made up of people from the tribes of Judeah, Benjaman, Levites and Cohans (which were scattered among all the tribes) but also families from some of the other tribes that were closer to the Kingdom of Judea.

Also, it was highly important, at the time of the Holy Temple, for a man to know if he was a Levite or a Cohan. For no other male (who were not of those two tribes) could be either a priest or work in the Temple in a religious capacity or in local areas to perform sacrifices on a daily basis. 

According to tradition and the law, if any male other than a Levite or Cohan dared to touch the Ark, it is said they would be killed instantly by one of the Holy Hosts.  If the Ark was to be carried, it could only be a Levite who could carry the Ark while the Cohanim would perform Priestly functions.  There were non Cohanim and non Levites who had to give Temple service, but only as layman and certainly they would not perform any sacrifices of any kind.  Their function would be more of helping out in the Temple cleaning up so that neither a Levite or Cohan could be considered unclean and have to go to a Mikvah (ceremonial bath) to clean themselves before they could do any priestly functions or go near the Holy Ark.

Over the years/centuries after the Temple was destroyed (70AD), it was important to know if you were a Levite or Cohan so that when the Messiah came and the Temple was rebuilt, Levites and Cohanim could then work in the temple.  Others were called Israelites (Children of Israel/Jacob/the "common man").

The only functions a Levite or Cohanim perform today are:

When going up for an Allyah (to recite the blessing of the Torah before the section is read on holidays, first to be called up are the Cohanim, then Levite and then everybody else.

When the first child is born and it is a male, and neither the mother or father of said child is not a Cohanim, they have a ceremony called Pinaben, where the parents buy back the child from a Cohan so that the child would not have to do menial service in the temple.

Cohanim also do a special benediction during holy days (i.e. Sabbath, High Holy days).  Because of their inherent holiness, Cohanim are supposed buried in a special part of a cemetery (Only the orthodox do that).  Cohanim are not suppose to be on a cemetery since cemeteries are considered unclean nor are they allowed to touch a dead body.  Only if a Cohan's immediately family is being buried are they allowed on a cemetery and if they do go, they have to perform a cleansing ritual at a Mikvah (ceremonial bath).

Only Orthodox and Conservative parts of Judaism still consider being a Cohan or Levite important. Other parts (i.e. Reform or Reconstructionalist) do not consider being a Cohan or Levite important. Hence if your family is not an Orthodox/Hassidic or Conservative, that information may not be passed down and lost.

You also mentioned that Israel is currently planning on rebuilding the Temple.  This would be impossible for several reasons.

 1) In order for the Temple to be rebuilt the Messiah (descendant of David would have to come)! Also the Holy Ark of the Covenant would also have to be found and returned to the land of Israel.  These two things are paramount in order to rebuild THE HOLY TEMPLE with the Ark residing in the Holy of Holy.

 2) In order to re-build the Temple, they would have re-build it on the site where the Mosque, the Dome of the Rock is currently.  I doubt the Islamic world would ever allow it, since the Dome of the Rock is the 3rd holiest site in the Islamic religion.

 3) Neither Orthodox/Hassidic or conservative parts of Judaism would allow the re-building of the Temple where they would have, again, sacrifices of animals and grains without the Messiah arriving and the Ark found! since it is a pre-requisite for the Temple to be rebuilt plus since the location is currently occupied by a major Mosque I would think that the gov't of Israel would even think about rebuilding THE HOLY TEMPLE

 It is said that the Holy of the Holy (the inner most part of the original Temple(s) were exactly over where the Holy Rock is and since Moslems wouldn't even allow Israeli archeologist to dig anywhere within, what is now part of the Mosque proper and outer courts, do you honestly think they would allow the Mosque be torn down and a Jewish TEMPLE take its place?  I doubt that very much; since you would be talking about World War III (remember Islam is currently the fastest growing religion!