Drugs can bind to more than one type of receptor, including receptors located in different areas of the body.
Example 1: The COX-2 enzyme is responsible for inflammation. Aspirin inhibits the receptor COX-2, decreasing inflammation, but Aspirin also inhibits COX-1 (which is similar in shape). COX-1 is responsible for maintaining mucous membranes of the body which protect the stomach lining from harsh bile acids. When COX-1 is inhibited, mucous membranes are of poorer quality, and stomach ulcers can develop. To sum: long term use of Aspirin WILL decrease inflammation (e.g. headaches, swelling, etc) but may ALSO affect another part of the body that was not 'sick' in the first place (e.g. the stomach lining).
Example 2: Anti-depressants often target the neurotransmitter serotonin. Anti-depressant drugs either increase the synthesis of serotonin, inhibits its recycling, or affect its receptor. The interesting this is that the serotonin that these drugs want to affect is in the brain, BUT serotonin and its receptors are also located in the gastrointestinal tract. Therefore it is common for people taking serotonin-related anti-depressants to also experience digestive disturbances.