The last total solar eclipse in Earth's history will occur in 200 million of years and will last a brief second. Historical eclipses provide useful data for measuring long-term changes in our planet's rotation speed.
The Moon is moving away from the Earth at a rate of 3.8 cm per year, there will come a time when, seen from our planet, the Moon will not be able to completely shadow the Sun. But you won't find a self-respecting astrophysics professional betting anything on this fierce prediction of geometry.