Ideally, one should serve good cheese with good bread. Some soft cheeses even make interesting substitutes for butter. For example, I recently bought a double-cream cheese from Fromager d'Affinois and spread it on my bread instead of butter. It was a nice change of pace. This French Brie-like cow's milk cheese would not have tasted well on a cracker.
Fromager d'Affinois is one of the biggest sellers of soft cheeses in the U.S. I recommend trying it.
If you are going to serve cheese with crackers, what kind of cracker should you buy? My two favorites are Reduced Fat & Sodium Breton wheat crackers and Red Oval Farms Stoned Wheat Thins. The former has a more buttery flavor than the latter. Sometimes I can tell that a cheese will taste better on the buttery Bretons. I wish I could give you a general rule for determining when to go with buttery crackers, but I cannot. Other cheeses go well with the more neutral, hearty Red Oval Farms crackers.
Good cheese crackers should not be flavored with garlic, herbs, peppercorns, too much butter, or too much salt. I don't even care for toasted sesame seeds. Strongly flavored crackers mask the subtle flavors of a good cheese. If you've bothered to purchase a good cheese, you should be able to enjoy its full flavor without distraction.
Both the Breton and Red Oval Farms crackers serve as fairly neutral platforms for quality cheeses. Although Carr's Table Water Crackers seem to dominate the cracker-upon-which-cheeses-are-put market, I think they have a bit less flavor than some types of cardboard. A good cheese cracker can be neutral without being completely tasteless.
I also think that Ritz crackers contain too much butter and probably too much salt. The right amount of salt is already added to most cheeses during the course of their production, so they don't need any extra from crackers. In addition, a lot of cheeses--e.g., Cheddars and especially any hard, dry cheese such as Dry Jack or aged Gouda--have a fairly high acid content. A high acid cheese on a highly salty cracker is an unpleasant combination.
My recommendation is to stick with either good bread or Reduced Fat & Sodium Breton wheat crackers and Red Oval Farms Stoned Wheat Thins. Happy munching.