Actually while diamonds and other gemstones are not nearly as heavy as gold they are enough heavier than common minerals to be captured in a gold pan or sluice box. Diamonds have been accidently found by many gold miners and almost all of the many diamonds found in California were recovered while placer mining for gold. Always be on the lookout for non-metallic minerals that seem slightly heavier than normal.
Tourmaline, garnet, diamond, chromite, rutile, barite, corundum, and zircon are all minerals that are heavy enough to be captured while panning for gold. Slightly heavier minerals include ilmenite, cassiterite, wolframite, scheelite, cinnabar. It is very common for gold prospectors to ignore anything not gold in the pan, and no doubt fortunes have been discarded as a result. As a rule, if it tends to hang with the black sand do what any good prospector does - be curious. When in doubt, collect it and find out what it is.
I had a personal experience with this recently as I was discarding what looked like little quartz pebbles but they kept showing up and kept settling in with the black sands. Turns out they were barite pebbles and I have a jar full of them now. Not worth a lot by themselves but could be if traced to the source. It is what they make drilling mud out of.
Garnet is a common placer mineral just like magnetite and when found in quantity is commonly referred to as "ruby sands" instead of 'black sands". They are not rubies of course, but it is worth keeping an eye out for crystal clear, gem quality garnet.
Wisconsin man finds 1.22 carat diamond while panning for gold - NY Daily News