Judaism considers marriage to be the ideal state of existence; a man without a wife, or a woman without a husband, are considered incomplete.
The Jewish concept of marriage is based on kiddushin (sanctification). The wife and husband are publicly sanctified to each other in an exclusive relationship. The rules regarding such sanctification, by definition, are for a relationship between the Jews. The Jewish declaration of marriage includes the phrase that the marriage is being carried out by the laws of Moses and Israel; such a declaration has no meaning for a marriage ceremony between a Jew and a gentile. If any such marriage is carried out Jews of course recognize the civil legitimacy of such a ceremony, but accord it no religious legitimacy.
Conservative and Reform Jews accept new minhagim (customs) in the wedding ceremony. At the giving of the ring the groom makes a declaration "You are consecrated to me under the laws of Moses and Israel". Traditionally there was no reciprocal response on the part of the bride. Today most Jewish women respond by giving a ring to the groom, and recite an appropriate passage, such as the famous verse from the Song of Songs, "Ani dodi v'dodi Li" [I am for my beloved, and my beloved is for me].
The marriage ceremony used to be one of acquisition. It is based on the rules for transfer of property in biblical times. In marriage, the woman accepts a ring (or something of value) from the man, accepting the terms of the marriage. A marriage contract (ketubah) is read publically. Witnesses are required for both the signing of the ketubah and the ceremony.
In the past, a Jewish marriage could be contracted in three ways: (1) with money (as when a man hands a woman an object of value for the purpose of contracted marriage, and in the presence of two witnesses, and she accepts); (2) through a ketubah (written declaration); (3) or by sexual intercourse, a method strongly discouraged by the rabbinic sages. Today only the marriage ceremony involving the ketubah is practiced.
Civil versus religious marriages, and inter-faith marriages
There is a difference between a religious Jewish marriage and the secular marriage. In the United States (and many other countries), when a rabbi officiates at a wedding, it is de facto a legal wedding by the law of the United States, as well; therefore, a rabbi cannot officiate for you without a civil license. This is the secular (civil) marriage. However, Kiddushin is a ceremony that takes place between two Jews. Most rabbis will not officiate at a wedding between a Jew and a non-Jew because it is outside the realm of Jewish traditional practice.
Under certain circumstances, Reform and Reconstructionist rabbis will officiate at a marriage between a Jew and a gentile, if the couple agrees to bring the children up as Jewish.
Halakha (Jewish law) allows for divorce. The document of divorce is termed a get.
Conservatuve Judaism follows most of the laws and traditions regarding marriage divorce as is found in Orthodox Judaism. One difference is that the Conservative movement allows certain changes to be made in the Ketubah (wedding document) to make it egalitarian. Often a clause is added to prevent any possibility of the women ever becoming agunah (called "the Lieberman clause"), or a t'nai (prenuptual agreement) is signed which has the same effect.
Reform Jews usually do not use a kosher Ketubah at their weddings; They instead use a short wedding certificate. They generally do not issue Jewish divorces, seeing a civil divorce as both necessary and sufficient. Conservative and Orthodox Judaism do not recognize civil law as overridin religious law, and thus do not view a civil divorce as sufficient. Thus, a man or woman may be considered divorced by the Reform Jewish community, but still married by the Orthodox or Conservative community.
Also see the entry on Religious_aspects_of_marriage for all religions.