In summary after completion of playthrough 1 and the DLCs there is a guaranteed total backpack capacity of 48, with a maximum possible capacity of 51 (if Claptrap Rescue: Lockdown Palace provides a backpack SDU).
Ned, The Secret Armory of General Knoxx and Claptrap's New Robot Revolution DLC there are an additional 3 Claptrap Rescue Missions to complete. With the addition of the Zombie Island of Dr. Each one is gained as a reward for completing one of the ten Claptrap Rescue Missions, for an extra thirty spaces of storage that can be earned throughout the game to a total capacity of 42 on the first playthrough. The Backpack SDUs each offer 3 additional slots of storage capacity.
3.2 Borderlands 2 and Borderlands: The Pre-Sequel.