Emergence is, itself, an emerging science. As such, there is disagreement among the scientific community as to what constitutes emergence. Here are some candidate examples.

Superconductivity. Individual electrons bounce about randomly, but in a superconductor they fall into a single rhythmic wave that can flow without resistance

Evolution. Random mutations that give certain individuals a reproductive advantage collectively lead to the evolution of a species.

Consciousness. Single neurons can't think, but together they form a web that gives rise to thought, memory, and personality.

Magnetism. In a magnetic material, electron spins align with their neighbors to give rise to a bulk magnetism.

Ants. Each individual ant follows simple rules, but together the ant colony has the capability of complex behaviors and grows as a single organism.

Traffic. Individual drivers stop and go depending upon the behavior of drivers nearest them. These simple interactions give rise to complex patterns, including traffic "crystals" in which drivers move as a slow-moving clump down the freeway, powerless to break the pattern.

Slime molds. Individual slime mold cells move on their own, but under certain conditions will combine together to form a single organism which moves as an entity.

Stock market. Individual investors follow simple rules to create a complex, self-regulating economic system.

Weather. Air currents and temperature combine to form powerful coherent systems, such as hurricanes and tornadoes.

The human body. The individual cells that make up our body are renewed every seven years, yet we remain ourselves with our personality and appearance.

Galaxy formation. Individual stars cluster together, attracted by gravity, into coherent shapes such as the spiral arms of the Milky Way.