Carboxylic Acids
Carboxylic acids contain a carbon atom with two bonds to one oxygen atom and a single bond to another oxygen atom in an OH or hydroxyl group (an oxygen attached to a hydrogen atom). They can donate the hydrogen ion from the hydroxyl group to a water molecule and thereby act as an acid. Carboxylic acids are the most common organic acids -- indeed, sometimes the phrase organic acids is used to refer to carboxylic acids. Everyday examples include citric acid, acetic acid (vinegar) and benzoic acid.
Phenols
Phenol is the parent compound of a class of compounds called phenols. All of them have a six-membered benzene ring with an OH attached to it. While much more acidic than most alcohols, phenol is only a very weak acid. Adding certain kinds of groups to the benzene ring, however, will make a phenol much more acidic. Picric acid, for example, is a phenol with three nitro or NO2 groups stuck onto the benzene ring. It was at one time used as an explosive, but it's so acidic and, therefore, corrosive it could eat through the casing in some artillery shells, so it was supplanted by trinitrotoluene (TNT).
Sulfonic Acids
Sulfonic acids feature a sulfur atom bonded to a carbon and to three oxygen atoms -- two of them by double bonds and the last by a single bond. The single-bonded oxygen is in turn bonded to a hydrogen. Just like the carboxylic acids, sulfonic acids can donate the hydrogen ion. They are very strong acids and are more rarely encountered in biological systems than carboxylic acids, although sulfonic acids are useful reagents for organic chemists.
Increasing Acidity
Carboxylic acids can be made more acidic by changes to the groups attached to the carbon atom. Attaching a group that withdraws electrons like a halogen atom, for example, will make the carboxylic acid more acidic, and the closer to the carboxyl group it is, the more acidic the carboxylic acid will be. Trichloroacetic acid, for example, is a much stronger acid than acetic acid. Adding electron-donating groups, by contrast, will make the carboxylic acid less acidic, which is why carboxylic acids with longer carbon chains tend to be less acidic.