Smells can be a great sign of danger, even when it comes from our own bodies. We've got here a story about a woman who smelled Parkinson's on her husband a good ten years before he was diagnosed. This spurred research into the subject, and we now have an idea of what the smell is and how it fits into the effects of the disease.
Tldr, it comes from the production of excess sebum, which contains chemicals known to be related to altered neurobiology associated with Parkinson's. The scent-sensitive woman who noticed it on her husband described it as earthy and musky.
Then there's the nick-of-time test for Maple Syrup Urine Disease. Although the disease can be verified with a blood test, symptoms could get so bad so fast that the time required for this testing becomes prohibitive. Luckily, it can also be identified by sweet-smelling urine, sweat and earwax.
Maple Syrup Urine Disease is a condition where the body can't break things down properly. If our body's natural defense system is inhibited so much that it can't break down the maple-syrup-molecule, for example, then we've got serious problems.
I am not a doctor so I don't know if this is the same smell/molecule, but Sotolon is the "maple syrup molecule." Other things could be exuding from the body, but this is a potent aroma compound, so it's easy to detect.
As a general rule, if you notice that you smell funny, it's something that should be checked out immediately. For example, fishy odor in the urine could be a sign of a urinary tract infection, and the smell comes from the bacteria living there (as opposed to the improper biotransformation of ingested molecules).
Then there's the cancer-smelling dogs, surely we've all heard of that. And for the record, if we interfaced with the world the way dogs do, with smell being way more important, and if we spent lots of time smelling all the things around us, including our own bodies, or those of our loved ones, we might notice these things too. But dogs get the credit, because honestly when was the last time you gave your partner a full body sniff-check?
Mar 2019, Inverse
Mar 2019, The Sun
Study about the smell of Parkinson's: