Certain classes of reaction will be readily apparent to you, too. Rusting (a certain type of oxidation) was already mentioned.
Another type of oxidation is what you would call fire. Specifically that's combustion in oxygen. You can also create fires that are burning using not oxygen but some other oxidizing species, such as fluorine, chlorine, or even nitrogen or carbon dioxide! For example, you cannot use regular CO2 fire extinguishers on certain fires (I think burning magnesium is one example) because the metal is so hot and reactive that it will burn even in CO2.
Solvation is also very common. Anytime you dissolve one thing in another thing this is a solvation reaction. The most obvious is salt in water, but really you do so many more without thinking about it. Soaps dissolve in both water and oils. If you use specialized household cleaners they often have chemicals in them for dissolving rust and other water-insoluble deposits. A nice exercise might be to go look at some household cleaners and read the ingredient lists and then go and see what the solubility properties of these materials are. When you make tea or coffee you are dissolving the most water-soluble portion of the leaves or beans in the hot water.