OMG, I demonstrated some of this stuff when talking to a GCSE chemistry class my local comprehensive a couple of years ago ( why do teachers insist that visiting professors demonstrate wacky stuff?)
The obvious one that occurs at room temperature is the solid-solid reaction between hydrated barium hydroxide and ammonium chloride. Most often, the experiment takes the form of mixing the two compounds in a small beaker sitting on an evaporating dish containing a small quantity of water at around 20 degrees C. The experiment should be performed in a fume cupboard due to the fact that ammonia is liberated. The reaction is endothermic and the water will decrease in temperature to about -20 degrees C. the fun part is when the beaker is picked up and the evaporating dish is stuck to the bottom of the beaker! Ammonium thiocyanate and a few other more unusual ammonium salts can be substituted for the ammonium chloride.
The other simple endothermic reaction that occurs at room temperature is the addition of baking soda powder to half a polystyrene cup of lemon juice. A thermometer is mandatory for this experiment.
There are many other room temperature endothermic reactions that occur in chemical engineering and even in biochemistry, but the reacting compounds are more complex.