Vanadium oxides are among the most promising materials that can be used as electrodes in rechargeable metal-ion batteries. In this work, we systematically investigate thermodynamic, electronic, and kinetic properties associated with the insertion of Li, Mg and Al atoms into rutile VO₂. Using first-principles calculations, we systematically study the structural evolution and voltage curves of Li_xVO₂, Mg_xVO₂ and Al_xVO₂ (0 < x < 1) compounds. The calculated lithium intercalation voltage starts at 3.50 V for single-atom insertion and decreases to 2.23 V for full lithiation, to the LiVO₂ compound, which agrees well with the experimental results. The Mg insertion features a plateau about 1.6 V up to Mg_0.5VO₂ and then another plateau-like region at around 0.5 V up to Mg₁VO₂. The predicted voltage curve for Al insertion starts at 1.98 V, followed by two plateaus at 1.48 V and 1.17 V. The diffusion barrier of Li, Mg and Al in the tunnel structure of VO₂ is 0.06, 0.33 and 0.50 eV, respectively. The demonstrated excellent Li, Mg and Al mobility, high structural stability and high specific capacity suggest promising potential of rutile VO₂ electrodes especially for multivalent batteries.