The word Orthodox is from the Greek combination of ortho which means 'right' or 'correct', and dox which means 'thought' or 'thinking'. The word is usually used in describing a religious group or set of beliefs.
There are various groups who have laid claim to the word orthodox as part of their titles, usually in the context of defining their group in contrast to another group who was not considered to be of 'correct thought'.
The Eastern Orthodox Churches hearkens back to what they see as the orginal forms of worship; for example, the Nicene Creed is used in its form as revised at the First Council of Constantinople in 381, in contrast to the the Roman Catholic church, which use the Nicene creed with the addition of the phrase 'and the Son' (see Filioque clause). This emphasis on the use of the original "creed" is shared today by all "eastern orthodox" churches.
Similar to this emphasis on traditional ways, the Russian Orthodox church is also known to promote the idea that the last Russian Czar and his family are "saints of true orthodoxy" and have preserved their faith to many people through their good works and belief in "orthodox christianity".
In English, the term Oriental Orthodox is sometimes used to refer to non-Chalcedonian eastern Christians, i.e. the Nestorians and Monophysites. (Of course, this term is impossible in some other languages, in which the word for 'Eastern' is 'Oriental'.)
The term Orthodox is also frequently used by Christians to refer to what they consider "mainstream" Christianity, as opposed to what they consider to be cults. This usage is especially popular among certain Protestant groups.