Acids are a little bit tricky-er than Hydroxides.
For example, take Hydrochloric acid...,
Hydrochloric acid is made by dissolving Hydrogen Chloride gas in water, when this happens, the HCl breaks up into ions in solution forming the acid solution, however, HCl gas is not ionic, the H and Cl atoms are held together with a polar covalent bond.
Another example,
Sulfuric acid is an aqueous solution of H2SO4, which is held together through the attractions between the H+ and SO4-2 ions. When H2SO4 is put into solution, since it is a strong acid, it will easily dissassociate completely into H+ and HSO4- ions, and then partially dissassociate again into H+ and SO4-2 ions (HSO4- is not as strong of an acid as H2SO4).
Another example,
Hydroflouric acid (HF) is made up of Hydrogen Flouride, a very ionic substance. Since Hydroflouric acid is a weak acid (because it isn't a strong acid) When HF is dissolved in water, only some of it dissassociates into ions.
But yes, for a very general case, acids are usually made up of ions since when they are dissolved, they will liberate H+ ions into solution, lowering the pH.