The Rutledge Edit
During the Cardassian conflict of the 2350s, Maxwell served as captain of the USS Rutledge, and was present for the massacre at Setlik III, wherein Maxwell's wife and children were killed. Maxwell's tactical officer at the time, Miles O'Brien, would later remark that Maxwell appeared to take the loss of his family remarkably well, not missing a single minute of duty. By the end of the conflict, Maxwell had been twice decorated with the Federation's highest citation for courage and valor. (TNG: "The Wounded")
The Phoenix Edit
In 2367, Captain Maxwell, believing the Cardassians to be re-arming and re-equipping themselves, undertook his own unauthorized preemptive strike, beginning with the destruction of a Cardassian outpost in the Cuellar system which Maxwell believed to be a military supply port disguised as a science post.
Eventually, Maxwell agreed to a meeting with Enterprise-D Captain Jean-Luc Picard, explaining that he had undertaken these unauthorized attacks because he did not trust the "bureaucrats" in Starfleet to take decisive action, an assertion to which Picard responded by stating his opinion that Maxwell was simply seeking revenge for the death of his family. Maxwell was also reunited with Miles O'Brien during his visit to the Enterprise and the two men greeted each other warmly as old friends. Maxwell also complimented the chief's abilities as a tactical officer. Miles expressed his own admiration for his former Captain.
Subsequent to Picard ordering him to travel to Starbase 211 under escort, Maxwell feigned compliance, but altered course en route, leading the Enterprise-D to another Cardassian vessel, which Maxwell claimed was transporting weapons in preparation for an attack on Federation space. Imploring Picard to search the ship in an attempt to prove his assertions, Maxwell threatened to destroy it, along with all hands. He was eventually talked down by Miles O'Brien who, by this point, was serving as the transporter chief aboard the Enterprise-D. Realizing that he had lost, Maxwell willingly surrendered to Picard, turning over command of the Phoenix to his first officer. (TNG: "The Wounded")
Background information Edit
Captain Benjamin Maxwell was played by actor Bob Gunton.
The script for "The Wounded" describes Maxwell as, "not at all what one might have expected. Slight of build, short greying hair, chiseled, angular face -- he could be Lenin. Or Lennon. But in the eyes there is warmth -- and humor. Creases at the edges testify to a lifetime of smiles and laughter. He is genuinely at ease with himself, and consequently puts others at ease." 
Author and writer Larry Nemecek noted that Maxwell's "Queeg-like turn" echoed Matt Decker from the Star Trek: The Original Series episode "The Doomsday Machine". (Star Trek: The Next Generation Companion, p.152)
The DS9 novel Force and Motion established that, after being incarcerated for nearly two decades, Maxwell was employed as a maintenance engineer on the private science station.