Here we report on the heritability and Intraclass Correlation Coefficients (ICCs) of brain volumes in 1,103 young healthy adults with mean age 29.2 years. Among them are: 153 monozygotic (MZ) twin pairs and 86 dizygotic (DZ) twin pairs, 133 non-twin siblings of MZ twins, 76 non-twin siblings of DZ twins, 335 siblings, and 81 unrelated individuals. ICCs were calculated between pairs of the following genetic groups: (1) MZ twins; (2) DZ twins; (3) MZ twins—their singleton siblings; (4) DZ twins—their singleton siblings; (5) siblings (SB); and (6) unrelated individuals (NR). We studied 4 brain groups: global, lobar, subcortical, and cortical brain regions. For each of 4 brain groups we found the same order of ICCs ranging from the highest values for MZ twins, statistically significantly smaller for the DZ twins and 3 sibling groups, and practically zero for NR. The DZ twins and 3 sibling groups were not different. No hemispheric difference was found in any genetic group. Among brain groups, the highest heritability was for the global regions, followed by lobar and subcortical groups. Only the cortical brain group heritability was statistically lower than other brain groups. We found less genetic control on the left hemisphere than on the right but no significant difference between hemispheres, and no hemispheric lateralization of heritability for any of the brain groups. These findings document substantial and systematic heritability of global and regional brain volumes.