As you would guess, there are many reasons a couple might go to couples therapy. An affair is often the breaking open of troubles in a relationship that spurs a couple to seek professional help. And it is often the case that problems had been simmering for a while before the affair started. There is work to be done about the affair but also about the relationship if this is the case. And there are other reasons couples seek help.
A number of couples have come for couples psychotherapy because they were not communicating as well as they would like, or not like the used to. This is a very good reason to seek therapy—the situation is usually not as bad and repair can happen with less work. But there is work to be done, change that would be important, when a couple comes for this reason.
Couples also come because of disagreements, and sometimes those disagreements are about disciplining the children. The task might well be in couples therapy to get the two to respect each other more and find a way that works for both of them better than what they are doing differently from each other. Other disagreements that have come to couples counseling include disagreements over: their estates (who gets what, who takes care of whom), how much drinking or chemicals one partner is using, time away from home by one of the couple, lying, spending differences, larger family issues (getting along with the in-laws, or the sister, or the parent, etc.), sexual frequency issues, betrayal (emotional, with pornography, etc.), religious conflicts (who goes to church and how often for example), along with many others you might be able to think of. Helping the couple to communicate more clearly, see their patterns, look to him/herself instead of the other can all be a part of the work to change disagreements. Helping the couple to get through a disagreement is a good step—many couples don't get through certain types of disagreements on their own, so helping them to get to a resolution is often helpful and can propel the couple into a better relationship.
Couples often don't like emotions, actually certain, specific emotions, in the significant other. They can often shut down an interaction or argument when certain feelings come up and then they never resolve the issue. Learning to allow the other to have at least part of what he/she is feeling can also make significant progress and growth for a relationship.
And couples sometimes come to couples therapy when one wants out of the relationship (whether she/he is saying that or not) and needs help of some kind to get to her/his goal: to end the relationship. This is a valid reason to come to couples therapy, though one of the two people is often unhappy with that goal. The therapist's job, in my opinion, is to help each person become healthier and help the relationship to be healthier, not necessarily to make sure they stay together. If the couple wants to make sure that they stay together, if this is one of the couple's goals, then the therapist will work towards that. If one or both want to end the relationship, the therapist will help the two work on the relationship, even if headed in that direction, watching for opportunities to make the relationship work better, not pushing the therapist's goals or values (whatever they might be), but helping the couple with theirs. This can mean that couples therapy, even successful couples therapy, may mean that the couple move apart and sometimes divorce.