Wearing gloves while examining a crime scene seems like a no-brainer to us, because we watch CSI and other acronym shows that follow modern police procedures. Anything you carry on your hands might contaminate evidence. But think about it: DNA wasn't used as evidence until just the last couple of decades. Gloves were used long before that. In fact, the turning point was a 1924 case in which Patrick Mahon stabbed and dismembered his lover, Emily Kaye.
Sir Bernard Spilsbury, a famous British pathologist, was called in as the chief medical examiner on the case. Spilsbury asked officers to collect the remains for further examination. Officers rolled up their sleeves and started tossing body parts into buckets, “as if they were sorting fish on a quayside.” Shocked, Spilsbury asked them if no rubber gloves were available, and they responded that they never wore protective gear of any kind.
By the next big murder case, Spilsbury had created the “Murder Bag,” a kit for police officers to carry that included rubber gloves, a magnifying glass, a tape measure, a ruler, swabs, sample bags, forceps, scissors, a scalpel, and other instruments. Suiting up with gloves before entering an active crime scene has been standard procedure ever since. The glove method isn’t the only thing the Mahon/Kaye case inspired, by the way—Alfred Hitchcock used details from the sensational story when he was making Rear Window.
From the narrative, one gets the idea that the gloves were more to protect the investigators than to protect the evidence at that point. You can read the gruesome story of that murder case at Mental Floss.