If you make a methylester out of the top OH you get codeine with antianalgesic, antitussive and antidiarrheal properties. Adding acetyl to both OH's gives the lipophilic form heroin, a highly addictive drug.
Morphine's structure is fairly complex. You have three condensed rings, an oxygen bridge and a nitrogen bridge. Before you scroll down you can try to guess its structure. Which rings are in the same plane? The key is to consider that the c-hexene ring is annexed in a cis configuration.
The benzene and c-hexane rings and the oxygen bridge are in the same plane. The c-hexene ring and nitrogen bridge are in a plane perpendicular to it.
The ring seen on top might resemble the terminal tyrosine of β-endorphin. Besides that the structure does not really look like the 31 amino acid peptide.
 You save o, m, and e. But it is arguable which o is taken out.
Well, jmol does not work anymore on my blog. But since so many people seem to be looking at this post, I'll try TwirlyMol. And if even that does not load, click here.