Supplements are particularly useful for supporting the liver if you consume alcohol on a regular basis. The two most well known are Artichoke Extracts and Milk Thistle. Artichoke Extracts contain a compund called cynarin which help the liver regenerate (and is particularly helpful if you have a hangover). Milk Thistle helps to protect the liver cells from the poisonous effects of excess alcohol and other toxins. So they are particularly helpful in repairing damage caused by alcohol. However, even if you do not drink, Milk Thistle can help the liver function better and produce more bile, which helps with bowel movements.
The less well known supplements for the liver are Garlic and Dandelion. Garlic helps the key liver detoxification enzymes to get to work. Dandelion also helps stimulate the detoxification processes and stimulates the flow of bile as well. However, these two supplements are not as specifically helpful to the liver as Artichoke Extracts and Milk Thistle.