Concise answer: All, or at least almost all life would be extinguished from the planet. So, yes sirree, Robert John, we would certainly notice the difference.

More involved answer:

Earth is rotating on its axis as a consequence of its formation. The nebula out of which the Sun and its retinue of attendant worlds formed collapsed and started to spin due to the torque induced on it by its local environment and by the motion of material toward the center. The conservation of angular momentum caused the spin to increase as this migration progressed. One will note that -with the exceptions of Venus and the tipped-over Uranus- the planets spin and revolve in the same direction.

Computer models suggest that soon after the proposed moon-forming collision with the Mars-sized Theia, Earth required five hours to complete one rotation. The moon’s gradual recession from Earth throughout the intervening eons has induced a dampening effect on Earth’s rotation. It now completes one rotation every 23 hours, 56 minutes. This rotation rate decrease will continue so that the day length will increase by 2.3 milliseconds per century.  So, Earth's rotation rate is decreasing, but at a glacially slow rate.  

Now, let’s imagine that Earth’s rotation instantly stopped for just 10 seconds. What would occur? The answer depends on location. Perhaps the most important effect would relate to the atmosphere. The gases are moving along with Earth. If Earth suddenly stopped, the gases would still continue to move. Regard people in a car moving down the freeway at 90 mph. If the car suddenly stops, the occupants will still be moving at 90 mph initially, hence the need for body restraining seat belts. The atmospheric gases would be under no such constraint and they’d move at their previous speeds even with our planet halted. The resultant wind speed would equal the rotation rate along any point.

Earth’s rotation rate is maximum along the equator: approximately 1036 mph. The rotation rate decreases with increasing distance from the equator.* The wind speeds along the equator would consequently equal about 1000 mph. Realize that the fastest wind speed ever recorded was only 253 mph** Wind force is proportional to the square of the wind velocity, so these equatorial winds would be at least 16 times more forceful than the fastest wind speed measured on Earth. Every structure and every person would be obliterated by these winds. The winds at most other latitudes would be immensely strong, as well. The wind speed would equal 253 mph at the high latitudes of 75 degrees N and 75 degrees S.

Another powerful effect relates to the oceans. Earth is not a perfect sphere, but is, instead, an oblate spheroid. The equatorial diameter equals 7,926 miles while the polar diameter’s length is only 7,900 miles. This oblateness is a result of the centripetal force induced by Earth’s rotation. Were that rotation to stop in an instant, the resultant deformation and subsequent resumption of the rotation would cause major shifts in the ocean waters. Unfathomably powerful tsunamis would scour the coasts all around the world.

Add to that the stresses induced in the landforms would produce devastating, city-obliterating Earthquakes and lava-hemorrhaging volcanoes.

While this answer provides only a cursory examination of the consequences, we can be well assured that if Earth suddenly stopped, we’d all perish in a cataclysmic confluence of assailing winds, inundating tsunamis and fracturing landforms.

Fortunately, we know of no mechanism capable of  abruptly stopping Earth’s rotation.

I hope this answer proves helpful.

*One can calculate this tangential speed with latitude with the following equation

Velocity = 1036cos(lat) mph

**At Barrow Island, Australia during Cyclone Olivia in 1996