Traditionally, wedding invitations include an invite for the friend or family member that the couple knows as well as a guest. The partners of friends or family in long-term relationships are usually named as this guest. Single friends or those in more casual or recent relationships are sometimes invited alone or may be invited with a "plus one" to accommodate a date.
Stick to the Rules
Stick to the rules of etiquette if you are thinking about bringing a casual date to a wedding. If the invitation does not specify a guest or a plus one, don't ask for an additional invitation or show up with a date. If you have been invited with a specific guest -- meaning that a person is named on the invitation -- don't show up with someone else because that person is busy or because you broke up with that person. A name on an invitation is not interchangeable with another name.
Consider Going Guest-less
If you've been invited with an unnamed plus one, then you can bring anyone you want to the wedding -- but consider the wedding's size and the couple's financial circumstances before making your decision about whether or not to bring a guest. A wedding is expensive, and receptions are often paid for on a per attendee basis. Couples may feel bad inviting single friends without a guest and so invite the guest as a courtesy, hoping you might, also as a courtesy, come alone. But if the wedding is big or if you know that finances aren't limited, then feel free to bring a date of your choice.
Remember, weddings aren't all fun -- the ceremonies can be kind of boring for those who don't know the couple, so if you do decide to bring a casual date, make sure you know the person well enough to gauge if he or she is likely to have a good time. Perhaps you think he'll like your friends who will be attending, or maybe she's interested in learning more about your family, or perhaps you want to fold the wedding into a weekend away. If so, give your date a brief synopsis of the people who will be at the wedding -- for example, a family tree if it's a family wedding -- so that your date can get a sense of who is who before entering the fray.
Although weddings are about a couple, it's okay to be single at a wedding. Many couples spend a lot of time creating tables and thoughtfully considering who will sit where -- they might seat single friends together. If you know the bride and groom well and your friends and family will be attending the wedding, it might be more fun to go alone -- that way you can catch up without having to make sure your date is comfortable and having a good time.