If there's one spot in invitation etiquette that causes the most contention, it may just be what names to put on the envelope. Suddenly your single friends are your favorites on the invitation list--their names don't give you hives worrying whether to put "Mr. and Mrs. Willaim Smith" or "Elizabeth and William Smith."

First and foremost, remember that most people are not going to be terribly angry if you don't follow the etiquette they prefer in envelope addressing. If you write something that isn't their preference, most will understand and assume it was an honest mistake. Remember, as well, that you don't have to follow the same protocol with every envelope. Traditionally, married couples were considered a social unit that was identified by the man's name. Clearly, many couples today feel that this is a touch one-sided, though many also either don't mind or prefer what they consider to be the more formal traditional approach. So, if you know or can reasonably guess your guests' preferences, write the envelope the way they would like. If not, use your preference! (After all, it is your event!)
If you choose to list both couples' names, it's considered correct to put the woman's name first. This holds true if she has the same or a different last name from her husband. So:
Elizabeth and William Smith
or
Mary Allen and Barton Davis
Titles may be used in addition. This gets kind of awkward with the ladies' first rule for the same last name (Mrs. Elizabeth and Mr. William Smith is fine to use but seems a mouthful to some) so that rule is often abandoned to get the more natural Mr. and Mrs. Elizabeth and William Smith. If ladies' first feels dated, list the person you know better first, list alphabetically, or list by whatever pleases your aesthetic sense. When in doubt, you can fall back on ladies' first because it's never considered incorrect.
Also, technically speaking, using "and" between two peoples' names is reserved for married couples. You may have long-term relationships or same-sex couples in your guest list who you consider having made an equivalent commitment; use "and" when you feel it's appropriate.
Again, technically speaking, traditional etiquette states that couples living at separate addresses get separate invitations. In the interest of saving paper and acknowledging long-term relationships that may not cohabitate, you may find it's more appropriate to send one invitation. We recommend sending it to the more organized partner...other than that, it's your call!
What about:
Same-Sex Couples: The only real question here is whose name comes first; in traditional etiquette, one lists the lady in a couple first. If you know one person better than the other, list his or her name first and his or her partner second. If you know them equally well, list alphabetically. Other than that, follow the rules you would follow for any other couple.
Single Guests: Let's start by defining "single." If a guest is not married but is in a relationship, it is polite to invite his or her significant other. If this is the case, list them both on the envelope, generally, one over the other. Say Amy Anders is your friend, and Joseph Caldwell is her significant other:
Ms. Amy Anders
Mr. Joseph Caldwell
If the guest is not in a relationship, you have a choice. Some couples choose to invite single guests with "and guest" so that they may bring a date. Others choose not to do so, which is not impolite if guests will know others at the event and/or that there will be other singles there. In this case, write
Amy Anders and Guest
If someone is in a relationship, do your utmost not to invite him or her "and guest." Their significant other has a name, and it's polite to use it!
A note on titles: I've used and not used titles with abandon in these example, and it's your choice whether to include titles. Titles make an address appear more formal. Consider the tone and formality of your wedding when deciding whether to include titles on invitations; when in doubt, it's never incorrect to use titles.
For more examples, more situations, and more general reassurance that you won't be flogged for the way you address your envelopes, please see http://www.twistedlimbpaper.com/addressing_etiquette.htm.
