A Wonderful Gathering mostly
The wedding is an opportunity to gather family and close friends to celebrate a momentous occasion. Most of the time people who are getting married want their guests to be there, but there are limits. Sometimes friends come in loosely defined groups, which means that some cannot be invited without including everyone. In addition, certain family members may include a particular unit of people, which may make it awkward to invite only certain members. Still, people want to enjoy their wedding and they don't want it to be ruined by particular individuals.
A few thoughts on how to specific who can bring guests to a wedding:
Invitation
The wedding invitation is usually the first step towards communicating with potential guests. While it is difficult to write, "do not bring this person", people may be able to put some controls into the document so that people have a sense that only particular guests are supposed to come. Granted, wording should be professional and tactful but firm and clear so that people are offended but still understand what is being said.
Personal contact
Of course, an invitation will not guarantee that certain people will leave their guests behind. Sometimes people have to conduct personal conversations with people in order to avoid particular guests. There are times that these conversations can be done in a subtle and indirect manner. However, there are certain situations that may require a more direct conversation. Granted, some of these conversations may be testy and uncomfortable, but for some people it is worth the awkwardness. People have to decide if a difficult conversation is worse than particular people showing up at the wedding.
Roundabout
Sometimes direct conversations may be a bit awkward, particularly coming from the bride or groom. There are times that it may work to ask certain individuals to have subtle yet firm conversations with those people who might bring an inappropriate guest. Of course, these conversations may also be awkward, but there are times where the wedding couple needs a bit of help. In some ways it is sort of like bringing in a "hired gun" to do some of the relational dirty work.
Kids
Sometimes people are not so much opposed to particular individuals, as they are concerned about certain groups attending. For example, people may like children in general, but perhaps they do not want them at the location of their wedding. In most cases, this can be communicated in the invitation. Again, there is a tactful way to state this, such as writing that the constraints of the facility or the nature of the event is best suited for adults. A polite request to leave children at home is usually understood by the typical wedding attendee.
Good with the bad
Overall, people have to decide how important it is to keep certain people away. Sometimes it is best to take the "good" with the "bad" in order to avoid conflict and hurt feelings. As mentioned, there may not be an easy way to exclude particular individuals without excluding a whole group of people that might include desired attendees. The balance is usually between individuals who can be largely ignored during the proceedings and those people who may be disruptive to others during the celebration.
Dealing with assumptions
Finally, people have to keep in mind that certain individuals will bring undesired guests even if wedding planners take steps to communicate restrictions. They will do this because they do not care, or they are oblivious to what has been communicated to them. Even though unwelcome guests can be a distraction, people have to take weddings in stride.
A wedding may be one of the most important days in people's lives but it will never be absolutely perfect so people should get as much enjoyment as possible without letting the little things ruin the experience.