Entering the U.S. with a specific intent to marry and then filing for Adjustment of Status
If you are a foreign national interested in marrying a U.S. Citizen, there are a few variables that you must consider before getting married.  The main issue revolves around whether you intend to marry prior to being admitted to / after entering the U.S.  If you had the specific intention of marrying prior to being admitted and then file for adjustment of status, you will encounter the the greatest of problems.  Remember that when entering the U.S. on a visitor visa or visa waiver, your purpose of coming to the U.S. is for a brief visit and to return to your native country prior to the expiration of your authorized stay.  Hence, if you intend to marry a U.S. citizen and then file for adjustment of status, you are not a bona fide visitor for pleasure.  As such, you are impliedly, if not specifically, misrepresenting your true intentions when you apply for entry to the United States.

Entering the U.S. to visit (with no original specific intent to marry) and then deciding to marry and file for Adjustment of Status
In this scenario, the foreign national is coming to the US to visit a friend, and after s/he has been here for awhile, the couple decides to get married and the alien files for adjustment of status.  In this situation, the foreign national is less likely to encounter the problem of the person who entered the US for the specific purpose of marrying and filing for residence.  However, in this situation, the alien should be prepared to show that he or she entered as a bona fide non-immigrant, either with a visa or on a visa waiver, and only decided to marry and file for adjustment after entry to the US.  Naturally, the more time that passes between the entry and the marriage, the easier it will be to prove non-immigrant intent at the time of entry.

Entering the U.S. to marry a US citizen, and then returning to foreign national's country to Consular Process
This situation is perfectly legitimate, but can often cause serious problems to the foreign national. The most obvious problem is that the U.S. Customs and Border Patrol (CBP) officer at the port of entry may not believe that the foreign national will in fact return to his or her country after marrying the USC.  Therefore, what often happens is that the alien is denied entry and must go back to his/her country and have a fiancé(e) visa petition processed on his/her behalf.

Entering the U.S., getting engaged, and then processing a fiancé(e) visa through the consulate
This is a common situation, and is perfectly legitimate.  The foreign national enters the US to visit his or her friend, and then they decide to marry. For various reasons, the foreign national does not wish to marry at this time, and wants to return to his/her country.  In this situation, the USC would file a fiancé(e) petition (Form I-129F) with USCIS.  Once the petition is approved, it is forwarded to the US consulate where the foreign national resides where s/he will apply for a K-1 visa.  Once the foreign national enters the US, s/he must marry the petitioner within 90 days and then file for adjustment of status with the USCIS office that has jurisdiction over the couple’s place of residence in the United States.  See our K-1 visa iKit.

US citizen travels abroad to marry alien, who will apply for an immigrant visa or a K-3 visa at the consulate
In this situation, the USC will travel abroad and marry the foreign national's country of citizenship.  Following the marriage, there are several options available.  The best and fastest is for the USC spouse to file an I-130 petition directly with the US consulate.  The problem is that some consulates do not want to be burdened with these petitions and, consequently, refuse to accept jurisdiction.  Therefore, it is important before making any definite plans, to speak with a consular officer to see whether they would be willing to entertain the I-130 petition.  If they do, then a consular officer will interview the couple and, if satisfied with the bona fides of the marriage, the petition will be approved.  At that point, the foreign national can begin processing the application for an immigrant visa to the United States.

If the consul does not wish to accept jurisdiction of the case, the USC petitioner would have to file the I-130 petition with the Immigration Service Center that has jurisdiction over the place of petitioner’s residence in the US. If the parties are not in a hurry for the alien to come to the US, they can wait for the Service Center to approve the I-130 petition and then forward it to the National Visa Center, and then the US consulate for processing of an immigrant visa.

However, if the foreign national wishes to come to the US more quickly, the USC spouse should also file immigration form I-129F, after filing the I-130 petition.  When this petition is approved, it will be forwarded to the consulate where the foreign national can apply for a K-3 visa.  Once the visa is issued, the foreign national will be permitted to enter the US.  After entry, the foreign national can immediately file for adjustment of status to permanent residence.