Q:

How might a colony treat the arrival of a new generation ship?

Assumptions

Space travel is hard.
Interstellar travel takes a long time.
Chances for a successful trip and colony becoming self-sustaining
are not considered super high.

Therefore, each colony will be seeded by 2 or more colony ships.
The Setting
Colony ship 1 successfully completes its voyage and despite extreme hardship and difficulties succeeds in establishing a self-sustaining colony and its infrastructure.
Decades later, colony ship $n$ arrives.
The Conflict
The crew and colonists of the first ship (rightfully) feel that they did the most difficult and risky part of the colonization.  They risked extinction and might feel that they deserve more rights or benefits within that colony's society.
When colony ship $n$ arrives, I'm sure the original colonists won't want to share all of the benefits of their labor equally.
The Question
Does this also encourage the development of a caste system (or even outright slavery) of the newcomers?
Bonus points:  

Would their be any difference in attitude towards colony ship $n$'s
crew vs. colonists?

A:

How the newcomers will be greeted depends on a number of variables.
State of the Colony

Is the colony living hand-to-mouth, or are they living in the lap of luxury?

If only a few decades have passed then chances are that the colony is still not too well off. The arrival of a colony ship stocked full of seeds, food rations, new equipment, spare parts, etc. would be seen as a massive boon.
In this case the space-travelers would probably be greeted with open arms.
If, however, they have a really good infrastructure/economy set up, but limited resources (such as not too much inhabitable land), and a few thousand new settles show up then that wouldn't really "work" for the colonists.
Colonist Culture, Political Ideology
How far removed from the original colonists are the people living on the planet? If they are in fact the same people who climbed aboard a colony vessel on Earth then they will share a deep bond with the people now arriving: they will have endured the same dangers of crossing interstellar space, and the same hope of starting new lives on a different planet.
In this case the two groups will be able to relate to on another. Furthermore, if the history of such groups meeting is to share resources freely then things will most likely go relatively smoothly.
However, imagine if the history of such arrivals is for the stronger group to simply enslave the weaker one. For example for the colonists to either seize the ship and use the new-comers as slave labor, or for the colonists, arriving with superior technology, to supplant the colony government and impose their own rules (imagine a new religion developing on Earth and sending out zealots to forcibly convert existing colonies).
Another scenario is that once arrived on the planet the colonists fall into anarchy, and the arriving ship finds an unstable political situation, with various groups claiming to be "the good guys", while they all secretly want to rob the travelers of their gear and enslave them.
The possibilities and their implications are too many to list.
Tech Level
If the colonists are several generations removed from the original settlers then the tech of the new-comers will probably be far more advanced than anything that could be found on the colony.
The new-comers could at that point offer their technology in trade, or simply use their might to crush the locals into submission.
Alternatively, maybe the original colonists counted some brilliant scientists among them, who developed tech which no one on Earth had ever even imagined. For example maybe the colonists form a culture of genetically modifying themselves in order to adapt to their planet, rather than terraforming it.
Maybe they find alien artifacts which mutates them, enslaves them, or allows them access to a hoard of tech of unparalleled power, but which they wish to keep absolutely secret because of its destructive potential. Again, there are countless scenarios.
When the seed ship arrives will they be absolutely shocked by the lifestyle that the colonists have embraced? Will they find a group of infected, alien-artifact-enslaved monsters like in Dead Space (the video-game)? 
This question is too freakin' broad!!!

"Songs of Distant Earth" by Arthur C. Clarke
I read a novel some years ago that dealt with a similar scenario.
--- Spoilers Ahead! ---
A colony had been established on a gorgeous planet some centuries before. Being very far from Earth, they did not communicate with their home-world. 
In the mean-time, a cataclysmic event causes a massive extinction event on Earth. In a last desperate bid to ensure the survival of mankind "seed ships" are launched into the void of space, hoping that the colonization of as many worlds as possible will ensure the future survival of mankind.
One such ship - which had been on its way to another world - finds itself heavily damaged by a meteor impact, and has to stop and replenish supplies on this world, which they weren't even certain still hosted a surviving colony.
They arrive with technology far more advanced than what the colonists have available. They run into language barriers, and more importantly, there are diseases which one group is impervious to, but have severe effects to the others.
Emotions run high. Many of the crew don't want to continue their perilous journey now that they know this colony is habitable, while others see it as their mission to go further and settle yet another world in order to ensure that mankind is as "spread out" in the universe as possible.
At the same time the natives are feeling exploited because they have to allow access to these outsiders to all sorts of resources that they could have extracted and used themselves.
In the mean time political leaders on both sides share the knowledge that if they really wanted to, the space-travelers have the weapons and gear to take anything they wish.
The space travelers end up deciding that continuing their journey is for the best, however your situation ends in the exact opposite way.

A:

Based on our own history, a lot will depend on where the nth ship comes from.
The settlement of North America has lots of examples to mine. Everyone had to undergo incredible hardships to arrive (sailing across the ocean in the 1500's was much like space travel today), but there was limited cooperation amongst the various groups that arrived in the New World.
Spanish colonists routinely fought amongst one another to gain power and influence, especially in seizing productive land from the natives. In the Spanish social system, becoming an aristocrat with titles and privileges was valued far above anything else, so we have numerous stories of Conquistadors leaving the Spanish Main to Central and South America with an arrest warrant outstanding from the governor of one of the islands. The hope was ence established with enough land and gold, they could go over the governor's head and appeal directly to the King of Spain. (Alternatively, they could now bribe the Governor and make their problems go away...).
Of course this only goes so far. Spaniards universally loathed the Protestants, so worked hard to eject English and French adventurers and would be colonists wherever they could.
English settlers came in two rather distinct waves, with the first major arrivals coming to establish religious colonies free from the corrupting influences of Rome and the Church of England. A second wave had a much broader base of speculators, landless people looking to better themselves and Protestant Dissenters. This group really established the foundations of the United States (Samuel Huntington's book "Who are We?" goes into this in detail). Other waves of British settlers who came later had different political and cultural backgrounds, so could settle in America, or in Canada, which has a different political culture than the United States.
The French were antagonistic towards the British and Spanish, and were also wildly ambitious, settling along the St Lawrence valley, moving into the Great Lakes region and then down the Mississippi river to modern day New Orleans. However, they ultimately lacked the manpower to fully develop their holdings, much less defend them, and were eventually ejected from much of North America.
For our purposes, the more similar the starships original culture, the easier it will be to integrate with the already established settlers. However, even small differences could lead to differentiation and even antagonism (i.e. Canada vs The United States).
If the founding culture is rent with internal instability, there is a possibility the culture in the colony star will be unstable and divided. If this is the case, the newly arrived starship could intervene on the side of one party and unbalance the power structure for their benefit.
IF the newly arrived starships have departed a long time after the initial colonization effort, there may come a point where the newcomers are so advanced they may simply impose their own will on the system, regardless of what the others think. This may be overt or subtle, depending on the newcomers (they may not even want to impose their system, but the attractions of their technology and culture might be driving the initial colonists to "convert").
So there is lots of room for various scenarios to play out, and mixing and matching different scenarios might be fun (a high tech, but divided and warlike culture arrives in a new starship, but the established colonists realize what is happening and start playing the newcomers off against each other...)

