BN86, what's the story on this? Where did you find it? It's certainly one of the most worn down coins, Wheat cent, or otherwise, that I've ever seen!
One of the most common ways is by the coin being used a piece of jewelry. One side hangs against the body and is continuously worn down while the other side receives little if any wear.
Although that coin in particular doesn't look like it's been a part of jewelery (not directly anyway) - but it certainly could have.
No story on that Lincoln cent, it was just something found in circulation (obviously it was in circulation a looong time). A big part of my coin collection is just random interesting things pulled out the change I get.
You actually can get a dateless 1916 Certified, there's enough differences in the design between a 1917 and a 1916 to do so.