We review recent advances in the study of the dissociative recombination of molecular ions with electrons with a primary emphasis on experimental studies. In particular, we focus on previous experimental measurements of recombination rates for N₂ ⁺, O₂ ⁺, and NO⁺ ions. In the context of this review, we present temperature dependent rate coefficients from recent merged beam studies of the dissociative recombination of N₂ ⁺, O₂ ⁺, and NO⁺ ions with electrons. Identifying underlying physical differences between the various experimental techniques enables a discussion of the effects of vibrational excitation on the dissociative recombination of these major ionospheric species of ions. For T < 1200 K, we conclude that the recombination rates for N₂ ⁺, O₂ ⁺, and NO⁺ ions in the ground electronic and vibrational states respectively are 2.2 × 10⁻⁷ (T_e/300)^−0.39 cm³ s⁻¹, 1.95 × 10⁻⁷(T_e/300)^−0.70 cm³ s⁻¹, and (3.5 ± 0.5) × 10⁻⁷(T_e/300)^−0.69 cm³ s⁻¹. Vibrational excitation is shown to play a significant role in laboratory measurements of these recombination rates. For each of these species, vibrationally excited ions yielded a lower recombination rate than the ground state. We also discuss the recombination of these species of ions for T > 1200 K.