A large number of currently prescribed drugs have been either directly derived from or inspired by natural products.
Some of the oldest natural product based drugs are analgesics. The bark of the willow tree has been known from antiquity to have pain relieving properties. This is due to presence of the natural product salicin which in turn may be hydrolyzed into salicylic acid.  A synthetic derivative acetylsalicylic acid better known as aspirin is a widely used pain reliever.  Its mechanism of action is inhibition of the cyclooxygenase (COX) enzyme. Another notable example is opium is extracted from the latex from Papaver somniferous (a flowering poppy plant). The most potent narcotic component of opium is the alkaloid morphine which acts as an opioid receptor agonist.  A more recent example is the N-type calcium channel blocker ziconotide analgesic which is based on a cyclic peptide cone snail toxin (ω-conotoxin MVIIA) from the species Conus magus.
A significant number of anti-infectives are based on natural products. The first antibiotic to be discovered, penicillin, was isolated from the mold Penicillium.  Penicillin and related beta lactams work by inhibiting DD-transpeptidase enzyme that is required by bacteria to cross link peptidoglycan to form the cell wall.
Several natural product drugs target tubulin, which is a component of the cytoskeleton.  These include the tubulin polymerization inhibitor colchicine isolated from the Colchicum autumnale (autumn crocus flowering plant), which is used to treat gout. Colchicine is biosynthesized from the amino acids phenylalanine and tryptophan. Paclitaxel, in contrast, is a tubulin polymerization stabilizer and is used as a chemotherapeutic drug.  Paclitaxel is based on the terpenoid natural product taxol, which is isolated from  Taxus brevifolia (the pacific yew tree).
A class of drugs widely used to lower cholesterol are the HMG-CoA reductase inhibitors, for example atorvastatin.  These were developed from mevastatin, a polyketide produced by the fungus Penicillium citrinum.  Finally, a number natural product drugs are used to treat hypertension and congestive heart failure.  These include the angiotensin-converting enzyme inhibitor captopril.  Captopril is based on the peptidic bradykinin potentiating factor isolated from venom of the Brazilian arrowhead viper (Bothrops jararaca).