There's a loose link.
Some variation on the events in the movie preceded the first episode of SG-1.
There have been several jokes that suggest that the O'Neil in the movie isn't the O'Neill of the show, however, the O'Neill of the show was on Abydos.
The planet Abydos is on the other side of the universe in the movie, but is in the Milky Way in the show, relatively close to Earth.
The Abydosians spoke a variant of Egyptian in the movie, almost everyone in the galaxy speaks English in the shows, and the Abydosians get more proficient in it each time they appear.
The Stargate on Abydos in the movie has different symbols than the Earth gate, but in SG-1 all the gates in the galaxy have the same symbols, except for the point of origin.
In the movie the Stargate just connects Earth to Abydos and back.
In SG-1 they generalized the idea into a galaxy-wide network of gates.
In the movie they don't show how they dialed the gate on Abydos, the shows invented the Dial Home Device (DHD) to simplify this.
If all you've seen is the movie, and you haven't sat down to watch any of the shows, start with SG-1.
The first episode of that picks up where the movie left off, and the first season will familiarize you with the basics of the Stargate universe.
Stargate Atlantis started airing at the same time as season 8 of SG-1, so they're happening at the same time, but with minimal interaction between the two shows.
Stargate Universe started after Atlantis ended, and can be watched after you've started Atlantis if you want to be up to speed (they recently had an Atlantis regular show up on Universe for an episode).
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There are definitely several links.
Here's a few of the main ones: Daniel Jackson Jack O'Neill
The pyramid-shaped starships The teleporter rings The resurrection chambers.
The Goa'uld (They aren't mentioned by name in the movie, but they do exist) Use of Egyptian Mythology
The staff weapons Abydos, and several of the people from Abydos (Sha're, Skara, and Yasuf, among others).
Major Kawalski from the original SG team is featured in the pilot and second episode and has some minor cameos in certain episodes.
Just for completeness, here's some major differences: In Stargate SG-1, most people speak English.
In the movie, most people speak Goa'uld, which is a variant of ancient Egyptian.
The actors who play all of the common characters are different, only Yasuf and Skara are played by the original actors from the movie.
The stargates on each planet had a different set of symbols in the movie.
In SG-1, they share the same set of symbols, for the most part.
The movie seems to take place in another galaxy, while the TV series indicates that Abydos is relatively close to Earth, only 25,000 light years.
The personality of O'Neill in particular is very different, the movie he is a much harsher person than the TV series.
Daniel Jackson seems to have fewer problems with allergies in the TV series than the movie.
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As it's been said, the link is tenuous.
It's almost better to think of the show as happening in a slightly different universe from the movie - there are some significant changes which don't really go against what the movie said or showed, but do go against what it implies.
They share the same basis, and the events of the movie ARE considered to have occurred prior to the start of the series.
The characters of the series would likely, if they watched the movie, consider it a dramatization of their (revised) official reports on the mission.
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Another difference not mentioned in the answer above is the nature of the Goa'uld: In the movie, IIRC, Ra is "the last?
member of a dying race".
In the show, he was just one of the Bad Guys.
In the movie, it looks like Ra, looking sorta like a real quadrupled (gray man stereotypical alien), "merged" with the host body, seemingly like a ghost?
This is based on the scene where the nuke blows up Ra's ship in the end of the movie.
In the series, Goa'uld are parasite snake-like creatures living inside hosts' bodies.
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There are also no Jaffa in the movie, they seem to use humans as slaves rather than the Jaffa as the guards have no head tatto.
But they do in the first season of SG-1.
So the Jaffa don't come into play till the pilot episode.
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I rewatched the Stargate movie recently, and it got me wondering about what I've been missing with regards to the TV series that have been spun off.  I enjoy reading people's opinions on which series is better, but I'm curious about what I'll be getting myself into when I start watching the episodes.  Is there any link between the movie and the shows, other than the namesake?
What sort of linkage is there between the Stargate movie and television universes?
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<stargate><stargate-sg1>
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The link is said to be loose and tenuous.  Some say that it is almost better to think of the show as happening in a slightly different universe from the movie. However, they share the same basis, and the events of the movie are considered to have occurred prior to the start of the series. There are several tenuous links between the Stargate movies and the series. The series appears to be in a slightly different universe. However, the events of the movie are considered to have occurred prior to the start of the series.
There are several tenuous links between the Stargate movies and the series. The series appears to be in a slightly different universe. However, the events of the movie are considered to have occurred prior to the start of the series.