The two classes of carbenes are singlet and triplet carbenes.  Triplet carbenes are diradicals with two unpaired electrons, typically form from reactions that break two σ bonds (α elimination and some extrusion reactions), and do not rehybridize the carbene atom.  Singlet carbenes have a single lone pair, typically form from diazo decompositions, and adopt an sp orbital structure.  Bond angles (as determined by EPR) are 125–140° for triplet methylene and 102° for singlet methylene.
Most carbenes have a nonlinear triplet ground state.  For simple hydrocarbons, triplet carbenes are usually only 8 kcal/mol (33 kJ/mol) more stable than singlet carbenes, comparable to nitrogen inversion.  The stabilization is in part attributed to Hund's rule of maximum multiplicity.  However, strategies to stabilize triplet carbenes at room temperature are elusive. 9-Fluorenylidene has been shown to be a rapidly equilibrating mixture of singlet and triplet states with an approximately 1.1 kcal/mol (4.6 kJ/mol) energy difference, although extensive electron delocalization into the rings complicates any conclusions drawn from diaryl carbenes.  Simulations suggest that electropositive heteroatoms can thermodynamically stabilize triplet carbenes, such as in silyl and silyloxy carbenes, especially  carbenes.
Lewis-basic nitrogen, oxygen, sulphur, or halide substituents bonded to the divalent carbon can delocalize an electron pair into an empty p orbital to stabilize the singlet state.  This phenomenon underlies persistent carbenes' remarkable stability.