What kind of births are recognized in Buddhism?
In the Theravada Abhidhamma, four different kinds of birth are recognized1, namely:


egg-born beings (Aṇḍaja), such as birds, fish and reptiles. 
womb-born beings (Jalābuja), such as mammals. Egg-born beings are also included in this category. 
moisture-born beings (Saṃsedaja), includes certain lowly forms of animals, such as worms.
spontaneously-born beings (Opapatika), such as petas and devas. These beings are generally invisible to the physical eye. 




1  Comprehensive Manual of Abhidhamma, Ch. 5: "Compendium of Matter", p. 256, by Ven. Bhikkhu Bodhi