No matter how tired you are, you should always remove your makeup at night before you go to sleep.
The chemical ingredients in your makeup tend to be drying, irritating, and comedogenic (can clog your pores). This in turn makes you susceptible to a nasty overnight case of acne, topical infections, and even non-specific dermatitis (what the dermatologists call a general skin rash). Use a gentle, non-stripping cleanser with a washcloth to make sure every trace of your makeup has been removed. Follow up with a nutrient rich moisturizer. Your skin will visibly show its appreciation to you in the morning.