So by looking at the male tail line-is this saying that the male's characteristics are more important in a breeding?
Many Boxer breeders seem to think so.

Certainly males have more opportunity to influence the breed, because they can produce far more puppies than a bitch can. However, breeding programs are built on bitches, not dogs. And not only do you want a great bitch in your kennel, but your best bet (especially if you're looking to keep a bitch puppy) is to breed her to a dog out of a great bitch - because you know he'll have her X chromosome, and will pass it on to his daughters.
For one to be considered a 'line' how many generations do they need?
This really varies, depending on how good the breedings turn out - some breeders breed for years but never really develop a line that carries any consistency. (It's harder now that the breed is well-established to develop a line, in any case, because most traits are fixed, with only a slight degree of variability in the grand scheme of things.)
How many original lines were there, and if that means they were line bred, does this mean there are a small amount of genetic individuals?
Well, the Boxer breed traces back to one specific bitch, Meta von der Passage; and a little further on, especially in this country, to the "four horsemen": Sigurd vom Dom, Dorian von Marienhof, Utz vom Dom, and Lustig vom Dom. These four Boxers were bred extensively and their children and grandchildren bred back to one of the four, or their children or grandchildren. The ABC has a Boxer history that contains much of this:
http://www.americanboxerclub.org/boxer_history.htmlSo, yes, we do have a rather small gene pool to begin with, and then we've had some bottlenecks (dogs that everyone bred to) such as Bang Away and Traper. The infusion of imported dogs, and the increasing availability of frozen semen from overseas, is helping to widen that pool a bit - other countries have had their own bottlenecks, of course, but they've been different from ours in many cases. (Plus those bottlenecks are getting further and further back, so may have less and less influence on future generations.)
What are some of the most well known lines famous for?
Hmm....well, Salgray has a pretty consistent head type, and Hi-Tech males tend to 'stamp' their look on their progeny (especially those descending from Arbitrage)....