Some creators and publishers choose to make time and space infinitely malleable. Others take readers to new times and places while leaving characters in a single timeline.
Time travel and alternate universes have become deeply-embedded narrative devices in the DC and Marvel comics universes. Particularly where you have a creative, and economic need, to perpetuate characters and story lines over decades and thousands of pages, the attraction of time travel and alternate, or parallel, storyworlds seems pretty clear: they give writers, artists, and publishers a pre-text for refreshing characters and narrative directions. New timelines or movement between time periods allows for characters to be re-contextualized, by either placing a familiar character in an unfamiliar setting or imagining how a character might have developed in different circumstances. The latter may extend to giving new life, or reviving, an otherwise "dead" character.
The comics of the Hellboy Universe demonstrate an alternative approach to bending time and space for narrative purposes. Stories in this universe take place in a single timeline and storyworld, but narrative continuity, beginning in the early '90s, is primarily preserved for the present, leaving decades, even centuries of history, in which to set other stories. These titles also map out a complex geography of people and events that allows for simultaneous stories in different places, both in the present and in the past. In this storyworld, time and space are bent for the reader, but not for the characters; there is only one historical Hellboy and only one Earth. When Hellboy is killed he finds himself in Hell, and thus far, there has been no coming back from that place.
To understand the difference between the Hellboy Universe and the Marvel and DC Universes, consider Trevor Bruttenholm, former director of the Bureau for Paranormal Research and Defense (B.P.R.D.) and also Hellboy's adoptive father. Bruttenholm is killed in the first story arc of the main Hellboy comics, "Seed of Destruction". Bruttenholm, however, resurfaces in both Hellboy and B.P.R.D., not through time travel or alternate universes, but by filling in history from before the '90s and the mainline continuity of the Hellboy Universe. Notably, the main Hellboy title is framed by a sliver of that history, which is the title character's emergence on earth in 1944. So, from the beginning, the Hellboy comics signal that there is, already, more to the story.
By contrast, if you look at Charles Xavier from the X-Men, a comparable mentor-type to Trevor Bruttenholm, Wikipedia currently lists 14 different versions of that character in various versions of the Marvel Universe. Furthermore, despite the "main" version's death in 2012's "Avengers Vs. X-Men" crossover, the character, in different guises, continues to resurface in present-day stories.
While Hellboy Universe stories set in the past are not entirely disconnected from present-day continuity, issues or mini-series set in past times and places are used to tell stories that are discrete and episodic, structured around a beginning, middle and an end. Certain characters may travel from stories set in the past to those set in the present, such as the Russian girl/demon Varvara, who first appeared in the B.P.R.D.: 1946 mini-series and is now part of the main narrative for B.P.R.D.: Hell on Earth, and others may travel from the present to the past, whether major, like Hellboy, Abe Sapien, and Liz Sherman or minor, like Lobster Johnson and Sir Edward Grey, but pre-continuity comics in the Hellboy universe are used to tell stories that are largely self-contained.
The setting off of past times and places from the present has also enabled particular artistic collaborations, such as those between Richard Corben and Mike Mignola, who have worked together on a couple of mini-series, "Makoma" and "The Crooked Man", and one-shots, "The Bride of Hell", "Hellboy in Mexico", and "Double Feature of Evil" set in the Hellboy Universe. These kinds of stories can be given a unique look and feel because they are their own narratives.
In addition to dealing with death differently, the aging of characters is also distinct in the single-timeline Hellboy Universe and the multiple-timeline Marvel and DC Universes. In the Hellboy comics characters not only stay dead within the main narrative, they are also shown to age in a more or less normal fashion (supernatural forces notwithstanding in the case of characters like Abe Sapien and Johann Kraus). By contrast, the extreme plasticity of time and space in Marvel's and DC's comics creates a context where characters can seem, effectively, ageless, even where, at some level, readers know that characters should be much older than they often appear.
American superhero comics have long been associated with youth -- the conflation of comics with superheroes being the main reason why the medium is seen as being "for kids" -- and that association still matters, even, if in many cases, this is more a matter of nostalgia for characters from formerly youthful readers than it is related to readerships that are actually youthful for Marvel and DC titles. Maintaining a historic chronology that seems more organic, that is, one where characters are represented as aging in a more or less natural way, where people die and remain dead from then on in the narrative, requires addressing those underlying questions of mortality. For the most part, however, the pliability of narrative time and space in DC and Marvel comics allows for such questions to be elided, leaving most characters in a perpetual, albeit vaguely defined, youthfulness -- forever toned and fit.
While Mike Mignola, and his collaborators like John Arcudi, Dave Stewart, Duncan Fegredo, and Guy Davis, have built the Hellboy Universe in part from the same stuff as Marvel's and DC's superheroes, they have also drawn on material which is seen as more "mature": folk tales, horror, weird fiction. Not only do these other traditions and genres incorporate themes of aging and death, but in the case of, for example, H.P. Lovecraft's fiction, Hellboy's creators are drawing on works where history and geography matter to narrative events and character roles. While the stories of the Hellboy Universe are largely set in the 19th, 20th and 21st centuries, the mythology in which the Universe is set stretches for millennia. The past matters here. In Marvel and DC the emphasis is on the present (which is one reason why character origins are periodically rebooted or retold to more closely reflect the experiences of readers at different times).
When telling stories about a core cast of characters over the course of decades, creators and publishers eventually need to address what would normally be the limits of time and space. For Marvel and DC the answer has been to rely on narrative devices like time travel and alternate worlds to create a context where time and space are flexible, enabling the constant refreshing of stories and characters. In the Hellboy Universe, readers are allowed to travel in time and across space, but characters remain planted in a single timeline. The past is made virtually infinite through small slices of narrative, while the present and the future continue to unfold in regular increments of interlaced continuity. Here the approach is to deepen and enrich what is known of the present through a further development of pieces set in the past.
While distinct, the adoption of these narrative strategies reflect creative challenges posed by the making of multiple ongoing serials set in shared narrative universes, challenges that are virtually unique to comics where the imaginations of writers and artists are free to run as far as and for as long as they need or want.
Splash image from the cover of B.P.R.D.: 1946 Issue No. 2, Dark Horse Comics