Carbonate + acid reactions - How to recognize these type of reactions? So I've got $$\ce{CaCO_3 + HCl \rightarrow CO_2 + H_2 O + CaCl_2}$$

I'm wondering how I can recognize these types of reactions? I know that when I mix an acid and a base I get salt and water but in this reaction there is also some $\ce{CO2}$ which is confusing me. When can I expect this type of salt base reaction and should I expect more like these with other by products other than $\ce{CO2}$?
The reaction you showed is actually a salt "exchange" reaction (also called salt metathesis), in which a salt is transformed into another one during the course of the reaction. In your example when calcium carbonate is treated with hydrochloric acid, calcium chloride is formed. At the same time, carbonic acid is generated and it spontaneously decomposes into carbon dioxide and water. The equilibrium is shifted towards the products due to the release of carbon dioxide gas from the reaction mixture, thus driving the reaction to completion.