If a person is not explicitly listed on the wedding invitation envelope, he or she is NOT INVITED. PERIOD.
The members of a couple who are dating but living separately should each receive his/her own invitation, and it is acceptable to invite one and not the other.
The members of a couple who are engaged but living separately should each receive his/her own invitation, and it is NOT acceptable to invite one and not the other.
The members of a couple who are living together are considered engaged (whether they are or not) and should receive one invitation, addressed to "Miss Donna Noble" <newline> "Mr. Lance Bennett". It is not acceptable to invite one and not the other.
A married couple should receive one invitation, addressed to "Mr. and Mrs. John Smith", or to "Ms. Gwen Cooper and Mr. Rhys Williams" if they do not have the same last name. If they have children and the children are invited, their names should go on the inner envelope, e.g. "Mr. and Mrs. John Smith" <newline> "Mary, Sara, and George". If the children are not invited, their names should be omitted from the inner envelope.
A single, divorced, or widowed man is "Mr. John Smith". A single woman is "Miss Rose Tyler". A widow is "Mrs. Peter Tyler" and a divorced woman is "Mrs. Jane Doe" (sorry, couldn't think of any Doctor Who characters who fit that profile
).
This is trumped where someone has a professional title, e.g. "Dr. Martha Jones" or "Dr. and Mrs. John Smith".
I'll shut up about naming conventions now.
According to Miss Manners, it's not necessary to include RSVP cards - the invited guest(s) "should" know that they should write a "yes" or "no" letter back - but in this day and age, if you don't include RSVP cards, you're going to be making a lot of phone calls.