The Blessed Buddha once said:
There will come a time, Bhikkhus & Friends, when all the mighty
oceans will evaporate, dry up, vanish, and exist no more...
But there will be no end of Suffering for beings who, blinded by
Ignorance and obsessed by Craving, are hurrying and hastening
through this samsaric round of endless rebirths...This I tell you!
There comes a time, when this mighty planet earth will explode in
a gigantic burst of fire, be completely destroyed, & exist no more...
But there will be no end of Misery for beings who, obstructed by
Ignorance and addicted by Craving, are hurrying, even running and
hastening from birth to repeated death in this round of rebirths...
This I explain to you!
 

Source:
Grouped Discourses of the Buddha. Samyutta Nikāya SN 22:99
http://www.pariyatti.com/book.cgi?prod_id=948507

http://www.accesstoinsight.org/canon/samyutta/index.html

 

For details on this Round of Rebirths: Samsara see:
http://What-Buddha-Said.net/library/DPPN/wtb/s_t/samsaara.htm
http://What-Buddha-Said.net/drops/II/Samsara.htm

Please enjoy study here for details on Rebirth:
http://What-Buddha-Said.net/drops/Rebirth.htm
http://What-Buddha-Said.net/drops/IV/Rare_Rebirth.htm
http://What-Buddha-Said.net/drops/IV/Divine_Rebirth.htm
http://What-Buddha-Said.net/drops/IV/Animal_Rebirth.htm
http://What-Buddha-Said.net/drops/III/Endless_Round.htm
http://What-Buddha-Said.net/drops/IV/Samsaric_Dread.htm
http://What-Buddha-Said.net/drops/IV/The_Minor_Hells.htm
http://What-Buddha-Said.net/drops/IV/The_Hell_Destiny.htm
http://What-Buddha-Said.net/drops/IV/Five_Destinations.htm
http://What-Buddha-Said.net/drops/IV/The_5_Destinations.htm
http://What-Buddha-Said.net/drops/IV/Kamma_and_Rebirth.htm
http://What-Buddha-Said.net/drops/IV/The_Samsaric_Round.htm
http://What-Buddha-Said.net/drops/IV/Mad_Demon_Rebirth.htm
http://What-Buddha-Said.net/drops/IV/Human_Being_Rebirth.htm
http://What-Buddha-Said.net/drops/IV/Hungry_Ghost_Rebirth.htm
http://What-Buddha-Said.net/drops/III/What_passes_on_by_Rebirth-Linking.htm