Step 1: Concept
The basicity of a dipeptide is determined by the $pK_a$ values of the side chains of its constituent amino acids.
Step 2: Meaning
Basic amino acids include Lysine (Lys), Arginine (Arg), and Histidine (His). Among these, Arginine has the highest $pK_a$ (approximately 12.5).
Step 3: Analysis
Glycine (Gly) is neutral. Glutamic acid (Glu) is acidic. Between Lys, Arg, and His, Arginine's guanidino group is the most basic functional group.
Step 4: Conclusion
Gly-Arg is the most basic dipeptide because Arginine is the most basic amino acid.
Final Answer: (C)