Immigration is actually a U.S.-centric term.  An immigrant is someone who migrates into your country, an emigrant describes someone who migrates out of your country, but the accurate term to describe this population from a global perspective is migrant.  It flies in the face of the U.S. citizen ego, but most migrants come to the U.S. with the intention of returning, and many do.  Migration describes their movements better than immigration does.

Princeton Professor and Director of the Mexican Migration Project, Douglass S. Massey, describes this trend in Mexicans in his essay "Seeing Mexican Immigration Clearly".

In keeping with these realities, Mexicans are not desperate to settle north of the border. Most migrants are not fleeing poverty so much as seeking social mobility. They typically have a job and income in Mexico and are seeking to finance some economic goal at home—acquiring a home, purchasing land, capitalizing a business, investing in education, smoothing consumption. Left to themselves, the vast majority of migrants will return once they have met their economic goals. From 1965 to 1985, 85% of undocumented entries from Mexico were offset by departures and the net increase in the undocumented population was small. The build-up of enforcement resources at the border has not decreased the entry of migrants so much as discouraged their return home. Since the late 1980s the rate of undocumented out-migration has been halved. Undocumented population growth in the United States stems not from rising in-migration, but from falling out-migration.

While I still expect opposition to using the term migrant, I will now turn towards the use of the word illegal.  I favor the views of Cuban Journalist Mirta Ojito.  She expressed them in an op-ed in the Miami Herald, "No Human Being is 'Illegal'".

"Illegal immigrant" is a term that no self-respecting journalist ought to ever use.  Not because it is politically incorrect, or inhumane -- though an argument can be made for both -- but because it is imprecise.

I discussed this term further with Mirta Ojito in an email interview and she wrote:

I think that whenever possible reporters should explain the circumstances in which the person came to the U.S.  For example, "such and such, who crossed the border illegally." Or, "such and such who overstayed his visa and is in the country illegally." ... What I'm trying to avoid is to label a person as illegal, to label the action, by all means but not the person.  It is the action that is illegal.

It is correct to label the action as illegal, but it is incorrect, even hurtful, to label a person as illegal.  I'm not going to discuss immigration law in this lesson, but it is important to remember that staying in the U.S. illegally is usually a civil penalty*, not a criminal one.  Driving over the speed limit is a civil penalty, as well, but everyone that drives 66 miles per hour on the freeway is not "an illegal".

Finally, we arrive at the term alien.  Alien is actually the correct legal term in the U.S. for someone who is born in or is a resident of another country.  The same arguments that I made against using the word immigrant apply to alien, but there is an additional problem with the word alien.  Even though it is a legal term, it is impossible to deny that the word "alien" has negative connotations.  For example, the word "alien" is often used to describe hostile invaders from outer space. 

Certain advocates suggest the word "alien" is the equivalent of a racial slur.  While I do not share this viewpoint, I do believe peoples have the right to determine their own identities.  I do not know of a migrant in the United States that likes to be called an alien.

This is the last time that I am going to entertain a debate about the terms used to describe migrants.  If people have a problem with my reasoning above, I will respond to criticisms in the comments section of this post, when I have the time.  From this point forward I will consider comments that rehash the same arguments as hostile and tangential to the issue I am discussing.

*UPDATE: See comments for correction details.