The legacy of Captain Marvel has continually progressed in the nearly four decades since his death, in large part due to the fact that his demise has (mostly) stood the test of time.
Which isn't to say that Mar-Vell has rested easily. His eternal sleep has been disturbed on numerous occasions. He appeared in the Realm of the Dead as a guide and ally to the Silver Surfer when Radd was feverish under the influence of a deadly virus. [Silver Surfer (3rd series) #63] When Grandmaster wielded the power of Mistress Death, he forced the Avengers to battle his Legion of the Unliving in the afterlife, including Captain Marvel among their foes. [Avengers Annual #16] The Grim Reaper created a similar Legion using dark magic, resurrecting Captain Marvel and several more dead Avengers as unholy zombie versions of themselves. This time, at least, the Legionnaires regained their senses and helped the living Avengers defeat the Reaper before returning to the great beyond. [Avengers (3rd series) #10-11] Captain Marvel and another team of dead Avengers were resurrected during the Chaos War, when Amatsu Mikaboshi began destroying the afterlifes along with the rest of reality. With the living Avengers trapped in a dream-like state, Mar-Vell led his comrades in defending their forms from the Grim Reaper. [Chaos War: Dead Avengers #1-3] Mar-Vell was also restored to life by the power of the Phoenix and mentally manipulated into serving a distant relative named Minister Marvel before once again returning to the grave. [Secret Avengers (1st series) #27-28]
Additionally, more than a half-dozen individuals have assumed Mar-Vell's identity as "Captain Marvel" or his role as Protector of the Universe in the years since he passed. Elysius grieved the loss of Mar-Vell and eventually decided to preserve him in a unique fashion using Titan genetic technology. She engineered a child, born of her and Mar-Vell's genes, whom she named Genis. The boy had an accelerated childhood (for fear of Mar-Vell's enemies striking at a helpless child) and grew up quickly while believing Eros and Elysius were his parents. He eventually learned the truth and assumed the power of the Nega Bands and the name Legacy. [Silver Surfer Annual #6]
Genis-Vell would slowly establish himself as a hero in the eyes of the universe and in his own mind, eventually taking the identity of Captain Marvel for himself. He had a rocky road to success, experiencing periods of insanity or dementia as he tried to cope with his inherited cosmic awareness. In one cosmic sequence of events, he encountered Phyla-Vell, his sister from another reality where Elysius chose to produce more than one heir to Mar-Vell. That reality was folded into the main universe, establishing Phyla as Earth-616's Captain Marvel as well.
Neither heir to Mar-Vell seemed fully comfortable as Captain Marvel, however. Genis later cast the identity aside to become Photon of the Thunderbolts, but his unstable powers led to him being killed by Baron Zemo as a potential threat to all reality. [Thunderbolts (1st series) #100] Phyla assumed another heroic legacy, claiming the Quantum Bands as the new Quasar, following in the footsteps of Mar-Vell's successor as Protector of the Universe. She briefly forged her own identity as Martyr, agent of Oblivion, but died in an encounter with Thanos (resurrected time and again, unlike Mar-Vell). [Guardians of the Galaxy (2nd series) #24] However, another version of Phyla has recently emerged from a parallel reality to take up residence in the 616 universe, still using the name Captain Marvel. [Infinity Wars crossover]
In addition to Genis and Phyla, Mar-Vell had a third child conceived the old fashioned way. Behind the scenes during the Kree-Skrull War, Mar-Vell and Princess Anelle of the Skrulls had grown close, and Anelle became pregnant by Mar-Vell. A Kree-Skrull hybrid was an anathema to both races, much less a royal one conceived by the Kree's greatest warrior. Anelle had the child heir to the throne Dorrek VIII smuggled out of the Skrull homeworld by a nursemaid. Dorrek was raised in secret on Earth under the human identity of Teddy Altman. After becoming Hulkling of the Young Avengers, Teddy learned the truth about his heritage. [Young Avengers (1st series) #9-12]
In addition to his children, Mar-Vell inspired other heroes to take up his name. The first was by accident, when a harbor patrol officer named Monica Rambeau gained electromagnetic powers and chose the super-hero name Captain Marvel without knowing about her predecessor. Monica operated as Captain Marvel with the Avengers for years, but later changed her name to Photon when Legacy claimed his father's title. (As mentioned above, Genis would later drop the title and change his name to Photon, hilariously stealing Monica's codename from her AGAIN. She changed her name to Pulsar before ultimately settling on Spectrum.)
Monica, Genis and Phyla had all passed on the Captain Marvel identity when the Superhuman Registration Act hit America, and the original Captain Marvel seemingly returned. The Initiative's Negative Zone prison '42' came across a rift in space that appeared to expel Mar-Vell from the past to the present, hailing from not that long before he learned of his cancer. Captain Marvel was isolated in the Negative Zone for a time, serving as warden to '42' to avoid a temporal paradox. He did serve on the side of Iron Man and the registered heroes during the final battle of the Superhero Civil War. [Civil War: The Return #1, Civil War (1st series) #7]
However, it was ultimately discovered that this was not the real Mar-Vell, but a Skrull sleeper agent, one of many acting as a herald to their secret invasion of Earth. The Skrull warrior named Khn'nr became lost in the honorable memories of his cover identity, and became reluctant to betray the ideals of Captain Marvel. He initially carried out a strike on Thunderbolts Mountain when the invasion began, but soon resisted his orders and turned against the Skrulls. Khn'nr died defending the people of Earth and passed on his mission of peace to Noh-Varr. A rebellious Kree ensign nicknamed Marvel Boy, Noh-Varr had declared war on the people of Earth for the destruction of his ship, but Khn'nr convinced him to aspire to a higher purpose. Noh-Varr did assume the identity of Captain Marvel, but unfortunately he did so as a member of Norman Osborn's dark Avengers after the invasion. When he discovered Osborn and the other Avengers were all criminals and villains, Noh-Varr abandoned them and eventually claimed a new identity supported by the Supreme Intelligence as simply “the Protector.” [Secret Invasion #6, Dark Avengers (1st series) #1, Dark Avengers Annual #1]
Of course, the most prominent and reigning heir to Mar-Vell's legacy remains Carol Danvers. Like several others mentioned above, Carol drifted away from the Marvel legacy for a time, leaving behind Ms. Marvel to form new identities as Binary or Warbird. She eventually returned to the name Ms. Marvel, however, and worked to forge a heroic identity of her own. Eventually, with the encouragement of Captain America, she claimed the name Captain Marvel for herself to carry on Mar-Vell's legacy. [Captain Marvel (7th series) #1]