Two-dimensional transition metal carbides (termed MXenes) are a new family of compounds generating considerable interest due to their unique properties and potential applications. Intercalation of ions into MXenes has recently been demonstrated with good electrochemical performance, making them viable electrode materials for rechargeable batteries. Here we have performed global screening of the capacity and voltage for a variety of intercalation ions (Li+, Na+, K+, and Mg2+) into a large number of M2C-based compounds (M = Sc, Ti, V, Cr, Zr, Nb, Mo, Hf, Ta) with F-, H-, O-, and OH-functionalized surfaces using density functional theory methods. In terms of gravimetric capacity a greater amount of Li+ or Mg2+ can be intercalated into an MXene than Na+ or K+, which is related to the size of the intercalating ion. Variation of the surface functional group and transition metal species can significantly affect the voltage and capacity of an MXene, with oxygen termination leading to the highest capacity. The most promising group of M2C materials in terms of anode voltage and gravimetric capacity (>400 mAh/g) are compounds containing light transition metals (e.g., Sc, Ti, V, and Cr) with nonfunctionalized or O-terminated surfaces. The results presented here provide valuable insights into exploring a rich variety of high-capacity MXenes for potential battery applications.