Flint and Obsidian (volcanic glass) are both ideal for creating edged weapons. Flint is also used in conjunction with steel to make fire. It's a fairly common milky-amber looking rock. Obsidian can produce *very* sharp, razor-like edges, but it's also brittle and tends to break easily. Flint isn't as easy to shape as obsidian, and takes a LOT of practice to create a good, even edge, but is more durable.
If you'd like natural materials a little more easy to shape, horn and bone can be ground against rough stone, concrete etc. to make a nice pointy nasty thing.