And now I, Nephi, do not give the genealogy of my fathers in this part of my record; neither at any time shall I give it after upon these plates which I am writing; for it is given in the record which has been kept by my father; wherefore, I do not write it in this work.
For it sufficeth me to say that we are descendants of Joseph.
And it mattereth not to me that I am particular to give a full account of all the things of my father, for they cannot be written upon these plates, for I desire the room that I may write of the things of God. 1 Nephi 6:1-3

Nephi claims that he did not include genealogies because he wanted to make room for more important matters.

Genealogies were important to Jews because they showed the pure Jewish line that came to Jerusalem.  It was used for inheritance and those who followed in the priestly line.  The Bible includes LOTS of genealogical lines with names and everything.

There could be a number of reasons why they are not included in the Book of Nephi.

• Genealogies are verifiable and easily traced, especially the line of Joseph.
• Genealogies are difficult to fake.  Lots of names to come up with and they can be confusing.
• There was no line of Nephi. 

These genealogies are spoken of as being very important and written on brass plates but the information is never revealed.  While there is some information of family lines, also known as "begatting," for the most part, the Book of Mormon only says "they begat sons and daughters."  Those children are nameless and untraceable.

1 Nephi 3:3
For behold, Laban hath the record of the Jews and also a genealogy of my forefathers, and they are engraven upon plates of brass.
1 Nephi 3:12
And he desired of Laban the records which were engraven upon the plates of brass, which contained the genealogy of my father.
1 Nephi 5:14
And it came to pass that my father, Lehi, also found upon the plates of brass a genealogy of his fathers; wherefore he knew that he was a descendant of Joseph; yea, even that Joseph who was the son of Jacob, who was sold into Egypt, and who was preserved by the hand of the Lord, that he might preserve his father, Jacob, and all his household from perishing with famine.
1 Nephi 5:16
And thus my father, Lehi, did discover the genealogy of his fathers. And Laban also was a descendant of Joseph, wherefore he and his fathers had kept the records.
1 Nephi 19:2
And I knew not at the time when I made them that I should be commanded of the Lord to make these plates; wherefore, the record of my father, and the genealogy of his fathers, and the more part of all our proceedings in the wilderness are engraven upon those first plates of which I have spoken; wherefore, the things which transpired before I made these plates are, of a truth, more particularly made mention upon the first plates.
Jarom 1:1
Now behold, I, Jarom, write a few words according to the commandment of my father, Enos, that our genealogy may be kept.
Omni 1:1
Behold, it came to pass that I, Omni, being commanded by my father, Jarom, that I should write somewhat upon these plates, to preserve our genealogy—
Omni 1:18
But it came to pass that Mosiah caused that they should be taught in his language. And it came to pass that after they were taught in the language of Mosiah, Zarahemla gave a genealogy of his fathers, according to his memory; and they are written, but not in these plates.
Alma 37:3
And these plates of brass, which contain these engravings, which have the records of the holy scriptures upon them, which have the genealogy of our forefathers, even from the beginning—

If the information was so important, and worth killing for, why isn't it mentioned here?  Genealogies are very important to Mormons today yet they are not important enough to include in these writings.