Are household cleaners generally acids or bases?
They can be either.
Cleaning agents ("CIF kitchen spray" and so on) are generally basic and contain substances such as sodium carbonate - these can react with oil and grease based dirt to form a soapy product that is easily washed away. They usually also contain a bleaching additive (perchlorate) to help with stain removal.
Those cleaning agents aimed more at limescale removal ("Grime and Lime" or "Viakal") will usually be acidic. The acid reacts with components of limescale which can then be washed away. The acid used is usually sulfamic acid - this is preferable to things such as hydrochloric, as it does not form chlorine gas if accidentally mixed with bleach.