It's a quaint story, full of sentimental value and focused on love and kindness, the birthday of the King.
Mary, an insignificant young lady, who cared about the things of God and was willing to do whatever He asked, was informed one day from an angel that she was going to have a child who was conceived of the Holy Ghost. The man that she was betrothed to, was informed in a dream from an angel that he was to marry her and that she would have a son whose name was to be Jesus, for He would save His people from their sins.
Speculation: It was likely that Mary's family and some of her friends thought she had committed fornication and was going to have a baby by someone other than Joseph. The only scripture to back up this speculation is that Joseph was minded to put her away privily. This indicates that at least Joseph was aware that she was with child, so it is also possible that no-one else knew this, or other circumstances corrected for this misunderstanding... however, this is not as likely.
A direct route from Nazareth to Bethlehem is roughly 90 miles. However, there was a problem with this route for the Israelites in the first century and a long time prior; this would have taken them directly through Samaria. Israelites hated Samaritans and so, would have traveled 120 miles and bypassed Samaria altogether. A caravan of this time period would have traveled about 20 miles a day, meaning Mary and Joseph would have been traveling for 6 days to make the trip.
There is no mention of a donkey in this story in scripture or any other historical documents. Caravans would have charged a fee to join them, and this could include the ability for Mary to ride in a cart. Otherwise, she would have walked.
Although Joseph was a carpenter by occupation, he was apparently not very wealthy. How do we know this? In Luke 2:24, Joseph and Mary offered the poor sacrifice, "And to offer a sacrifice according to that which is said in the law of the Lord, A pair of turtledoves, or two young pigeons." This references the law in Leviticus 12:5-8 regarding the sacrifice "when the days of her purifying are fulfilled". Verse 8 says, "And if she be not able to bring a lamb, then she shall bring two turtles, or two young pigeons;"
The word "turtles" in the English JKV is really an abbreviated translation for "turtledoves". This is more evident in the Catalan Trinitarian Bible Society translation which uses the word "tórtores" in both Luke and Leviticus. The Strongs concordance confirms the meaning of this word, תּור tore
which is translated "turtledoves" in several other places in Leviticus.
This means Joseph likely would not have been able to afford a donkey or cart of his own.
Now we come to a very odd distortion in the story, the reason for the trip. This requires some background.
Caesar Augustus could possibly be considered the most successful ruler in all of history. His reign began at a time when the roman empire was in collapse. There had been civil wars, assassinations, and many other demoralizing events throughout the empire. He was able to start with the kingdom in that condition, and bring order and power out of it, establishing both a very solid economy and military. 
Caesar Augustus mandated two census', also referred to as worldwide taxes. Luke 2:1-5 explains that Joseph went to Bethlehem for a taxing which was first made when Cyrenius was governor of Syria. Cyrenius was the governor of Syria during the first of the two census' by Caesar.  Joseph went to Bethlehem because he was of the house and lineage of David. It is possible then that Joseph had family in Bethlehem, because that was the point of the trip, to go to the town of his heritage.
Caesar was a good emporer who had helped the economy in many ways. This taxing was not overbearing, but rather was more of a census. This required people to go back to the home of their lineage. Rather than people hating this census, it is more likely that the general population was in favor of it. It is hard to say without further research into this time period and the history of Caesar's reign.
Mary and Joseph were both descendant from David. Matthew chapter 1 shows the lineage of Joseph, and Luke chapter 3 shows the lineage of Mary. We know Luke is speaking of Mary, because it says in verse 23, "And Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was the son of Heli," As usual, the Catalan is much closer to the original text in this verse, saying "de Josep, d'Helí". The words the son are not in the text, but rather it simply says that Joseph was 'of Heli' which could mean he was the son in law of Heli. Because the Matthew account specifies that "Jacob begat Joseph" we know that Luke is showing the lineage to Mary.
Joseph was a descendant of Solomon, and Mary was a descendant of a different son of David, Nathan. There were 28 generations between David, and Mary and Joseph, so they were very very distant relatives.
After a 6 day journey, Mary and Joseph needed to find a place to stay. They would spend at least 2 years in Bethlehem before making another journey. Luke 2:6 "And so it was, that, while they were there, the days were accomplished that she should be delivered." There is no reference that specifies how long they were there before those days were accomplished, but it does indicate that they had a few days to settle in before Mary had the baby.
Luke 2:7 "And she brought forth her firstborn son, and wrapped him in swaddling clothes, and laid him in a manger; because there was no room for them in the inn." The inn, κατάλυμα
From καταλύω; properly a dissolution (breaking up of a journey), that is, (by implication) a lodging place: - guestchamber, inn. (Strongs Concordance)
A lodging place or guest chamber. The term in Luke 2:7 is singular; there was only one place that was considered. No more details are given, so this part of the story is left to speculation. We know that there wasn't such a thing as a hotel in those days, and Bethlehem was not a very large town. Did Joseph or Mary still have relatives living in Bethlehem? It is very possible, but 28 generations had obviously spread people abroad. This guest chamber could have been in the house of a relative, but again, this is only speculation.
Now we come to the most important part of the story; the part that has been lost in time.
Luke 2:11-12 "For unto you is born this day in the city of David a Saviour, which is Christ the Lord. And this shall be a sign unto you; Ye shall find the babe wrapped in swaddling clothes, lying in a manger."
Which manger? There were certainly many mangers throughout Bethlehem. How did the shepherds know where to go? There is no record of the angels telling them where this would be. This is where we have to look at the part of the story that is taken out; the record of the birth of Christ, by Micah.
Micah 4:8 "And thou, O tower of the flock, the strong hold of the daughter of Zion, unto thee shall it come, even the first dominion; the kingdom shall come to the daughter of Jerusalem."
What was Micah talking about here? In Micah 5:2, just a few verses later, "But thou, Bethlehem Ephratah, though thou be little among the thousands of Judah, yet out of thee shall he come forth unto me that is to be ruler in Israel; whose goings forth have been from of old, from everlasting."
Micah is explaining in detail where Christ was to be born. The tower of the flock, מגדּלה עדר migdâl ‛êder. There is a real tower, standing today on the north side of Bethlehem, facing Jerusalem, known as Migdal Eder. This tower was the place where sheep who were about to lamb would be brought to give birth. These lambs were the lambs intended for sacrifice in Jerusalem. The perfect, unblemished lambs were wrapped in swaddling cloth to protect them from hurt, damage, blemish or injury.
Where else in the world would be a more perfect place for the perfect, sinless Lamb of God to be born? Wrapped in swaddling cloth, as a sign of the purpose of His coming, born in the same manger that many sacrificial lambs were birthed.
How could this vital part of the story be left out? Why has the story changed so much from what we are told in the scripture? The traditional story tells us of the birth of Christ, of the angels and the shepherds, and of the glory and praise that was given to the newborn King. What it doesn't tell, is why He came. By leaving the tower of the flock out of Christmas, the purpose for His coming can be forgotten. You see, we've taken the cross out of Christmas.
Jesus Christ was born to die. He came to give His life for our sins and free us from the bondage of sin - death and hell. In even more significance and quaint sentimental value than the story we were told, He came as a Lamb for sacrifice.
This Christmas, let us not forget the most important part of the story: why He came.