Decaffinaton of coffee beans
A salt water fish shrinking in fresh water, a fresh water fish expanding in salt water
Distillation of spirits (alcholic beverages)
Fractional distillation of crude oil
None of those are chemical equilibrium. Chemical equilibrium is where the rate of the forward reaction equals the rate of the reverse reaction: products equal reactants.
Caffiene is extracted with methylene chloride and/or ethyl acetate. Not really an equilibrium reaction, just a organic extraction. Distillation is just that, a distillation. If it were to reach equillibrium you woul never get the thing distilled. Ditto that with ethanol.
That fish thing is kinda an equilibrium, but not a chemical equilibrium. That would be osmosis where the salt tries to become 'equal' on both side of the membrane; and this membrane would be a fish.
One example is the methanation production using carbon dioxide and hydrogen gas to yeildl water and methane. Where the methane, in turn is used as natural gas (bunch of sulfide/thiol compounds in there as well).
Dissolved salt in water is another one. NaCl in an aqueous solution gives Na+ and Cl- , the two dissociated ions are in equilibrium.
Basically any acid and/or base will be an example of chemical equilibrium. And, that would go for many biological systmes; most fluids (eg blood) in your body are buffer solutions and are at chemical equilibrium.