The main reason people immigrated to the United States was economic. Consider the Irish Famine, for example. It is a good example of how poor many lower class workers were, and how close they were to the edge. Many came to the United States for the same reasons they always had. There was free land for homesteaders after the Louisiana Purchase greatly increased the amount of land the US had to give away.
The Irish represented the largest wave of immigrants, and they came first because of political and economic oppression in their homeland. They came, of course, in largest numbers in the wake of the potato blight and subsequent famine that began in 1845. Over 2 million Irish people entered the United States during the 1840s alone, and over 8 million arrived between the 1820s and 1880s. Their experiences were mixed. Many found jobs in the enormous infrastructure building projects of the 1820s and 30s, specifically canal digging. Many settled in cities and took manufacturing jobs, and others took service jobs meted out by political machines, like police officers and firefighters. After the Civil War, in which the Irish participated in enormous numbers, many recent immigrants went to work building railroads.
There were two major reasons for coming. There were economic problems. The most famous of these was the Irish potato famine. There were also political problems. The most famous of these were the revolutions of 1848 that caused many Europeans (Germans in particular) to leave their countries and come to the US. They left because they feared persecution for their parts in the revolutions or because they simply were unhappy the revolutions had failed.