Large-scale self-consistent multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations are reported for the n <= 6 levels in Be-like ions from B II to Ne VII. Effects from electron correlation are taken into account by means of large expansions in terms of a basis of configuration state functions, and a complete and accurate data set of excitation energies; lifetimes; wavelengths; electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole line strengths; transition rates; and oscillator strengths for these levels is provided for each ion. Comparisons are made with available experimental and theoretical results. The uncertainty of excitation energies is assessed to be 0.01% on average, which makes it possible to find and rule out misidentifications and aid new line identifications involving high-lying levels in astrophysical spectra. The complete data set is also useful for modeling and diagnosing astrophysical plasmas.