Stargate SG1 is a Sci-Fi adventure TV show that was premiered on Showtime on the 27th of July, 1997 and then moved to the Sci-Fi channel and for full 10 seasons. The show is based on 1994 Stargate film by Dean Devlin and Roland Emmerich.

The plot of Stargate SG-1 as per Wikipedia "picks up a year after the conclusion of the events recounted in the original feature film. It follows the present-day adventures of SG-1, a military team from Earth. SG-1 and a dozen other SG teams venture to distant planets using a fictional alien portal known as a Stargate, which in the series is housed in a top-secret United States Air Force military base known as Stargate Command (SGC) in the underground Cheyenne Mountain Complex in Colorado Springs, Colorado. In the first eight seasons, the mission of the SG teams is to explore the galaxy and search for alien technology and allies to defend Earth against the Goa'uld, a snake-like parasitic alien race that takes humans as unwilling hosts. As explained in the series' backstory, the Goa'uld had transported human slaves from Earth to other habitable planets across the galaxy thousands of years ago and now pose as gods of old Earth mythologies, particularly Ancient Egypt. SG-1 eventually learns that highly evolved human-like beings, known as the Ancients, had originally built the Stargate network millions of years earlier, before ascending to a higher plane of existence, after which they pledged not to interfere in the lives of other species. The Ori, a faction of the same race as the Ancients who instead use their powers to subjugate other species by religious indoctrination, assume the role of the main antagonists in seasons 9 and 10"

So why HBO, Stargate is a great show, it has huge material, great characters, excellent ideas and creative plot, what it does have is good special effects, what HBO can add is excellent cinematography and adult approach for the show. (Imagine the war at the end of season 7 with HBO effects :)

To be clear, we are not looking for Stargate Atlantis or Stargate Universe, we are looking for the same Stargate SG1 characters, similar plot, same idea and most importantly, the happy sarcastic tone of the show and we are for sure not looking for another GoT :)