I ran Shadowrun from 1999 to 2007, encompassing both SR3 and SR4 rule sets.
THE ORIGINAL CAMPAIGN - SR3Prologue:I had been running for years a Forgotten Realms AD&D 2nd Ed. campaign with a large group of adult players who were mostly DM's in their own right and we played every Sunday, rotating between our different worlds. Between us we had Forgotten Realms, Spelljammer, Dragonlance, Planescape and Al Qadim. I was itching to do something different (and frankly needed a break from my complex FR world) and had been getting more and more into reading cyberpunk type novels. I discovered some ads in different gaming journals about Shadowrun and was intrigued. No one in my group except one had ever heard of it or played it and the one person had only played a few sessions way back in SR1. When I checked it out at my FLGS, I discovered SR3 had jsut been released. I bought the BBB. I had to spend a week visiting a friend in TN the next week and I took the book with me and taught myself the system late at night and while he was workign during the day. I came home, got the players enthused and helped them create characters in a new system.
Set-up:My initial campaign was "traditional", set in Seattle and encompassed the majority of traditional archetypes as PCs: An elf adept, an elf infiltrationist, a dwarf rigger, a dwarf sammy, a dwarf weapon specialist, and a human private eye/face.
The Meat:I ran a strong mix of personal adventures and pre-gen adventures such as Mercurial, Bottled Demon, Paradise Lost, and many of the other classics. These storylines were all updated to match the timeline in which I was running (SR3: Early - Mid 2060's.)
There were also original storylines playing out as well: A brewing civil war in Tir Tairngire with involvement with the "rebels", fall-out from dealing with Perianwyr, a quasi-legal front that was a waste removal service, and saving downtown Seattle from a nuclear bomb in the hands of some right wing terrorists.
The runners were "retired" by being left trapped in the Renraku arcology when it shutdown. This is when I transitioned to the SR4 ruleset and an entirely new campaign. As far as I know, they are still leading a little band of survivors looking for an exit.

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DA TROLLS (AKA The Redmond Barons) - SR3Set-up: This campaign I ran concurrent with the above group. It was a Troll Go-gang in Seattle. They were heavy on cybered up muscle, with one rigger, one adept and one low-end mage. After a few months of runnig hte Originals and getting rather intricate storlines going, it was frustrating when one or more core players couldn't make the regualr Sunday session. This began as a suggestion by several of the players as "something to do" when the whole group couldn't be there for the normal Sunday session and we didn't want to leave them out of the current storyline. ("We could all play Troll Gangers! On bikes!" "Yeaahhh!!")
The Meat:It started out as being mindless action with little "continuity." I improv-ed most sessions with little more than a page or two of notes on some ideas and NPCs. The players took to it, tho' and it quickly became a favorite, almost eclipsing the "real" campaign.
There were bar fights, clashes with other gangs, skirmishes with The Ancients, managing and bankrolling an up and coming orc thrash band with a breakout troll female vocalist who was a prostitute freed from her pimp. There were Lonestar wiseguy intrigues, jail/prison breaks,a relentless Lonestar captain out to take them all down, and being muscle for the Yaks. They also became celebrities in a popular fighting game/ sport called Turf War (sponsored/working for the Yaks, of course.) The characters were never officially or unofficially retired, I jsut stopped running them as I was completely focused on running the new SR4 campaign and always actually meant to go back to them again someday.
NOTE: I actually ran Turf War officially at Gencon in 2004, I think, as a multi-day tourney with troll pre-gens and teams of 6 players each fighting each other to make it to the finals. There they competed against the 3 Time Champions, The Redmond Barons, from my home-game for actual gift certificates for SR products at the booth in the Dealers Hall. Several of my players were good enough to play their own characters there for the final round. It was a blast.
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DENVER - SR3Prologue: After a couple years of running the above two campaigns, I purchased a used copy of the Denver Boxed Set. I read it and fell in love with the setting. I convinced a portion of my gaming group that it would be jsut smashing to create new characters and play in yet another campaign in Shadowrun.
Set-up: It featured a (nearly) all magic lineup: two mages, a shaman, an adept and a troll mundane sammy/weapons specialist. Being that magic intensive was something new for me and the players.
The Meat:The runs were somewhat traditional with an emphasis on coyote runs (ferrying people/things across the borders). There was a save Denver from a mad scientist at a lab run. I also adapted a pre-gen, One Stage Before, to being set in Denver And they were frequently working for a Dragon, at first unaware he was their Johnson but slowly getting bits and pieces.
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THE MARSHALS - SR4Prologue:SR4 came out in 2005 and I picked it up at it's release at Gencon. I took the book home and read through it, liking most of the changes to the system. However, I was running three other campaigns simultaneously, all with SR3 rules. I wasn't about to convert the old games over to the new rules. I sure as heck wasn't starting a 4th concurrent campaign!! So, the book went on the shelf. Then, about 4 months before Gencon 2006, I discovered the Gencon tourney was using SR4 rules.

I bit the bullet. What other way to learn the rules to play in the tourney than ... yeah. "Hey guys, I think we should start up a new campaign. No, really! Using 4th edition. C'mon, it'll be great. I have some ideas to make this really stand out. You are gonna love SR4! Fine, I tell you what... we'll co-create characters and play a session or two. If you like it after that, I'll buy you all a copy of the rule book." So, with bribery I managed...
Set-up:...to bury myself in a hole. What the hell was I going to do
different? They've already played SR for years.... lottttssss of SR... They've been thieves, assassins, gangers, mercs... They've kidnapped immortal elves for pete's sake. What could they possibly do different? How many cops can you shoot before... wait... cops. They can be COPS! Lonestar Detectives. The loser division working lousy Vice cases.
Lets see... one can be an ex-SWAT team member, relieved from his SWAT team for getting his partner killed, one a forensic specialist disgraced for mishandling evidence, one can be an ex-undercover drug detective, an orc, that blew his cover and also has a little drug habit of his own... one can be internal affairs looking into the undercover guy on the sly. One can be a rookie jsut making detective... a troll that failed his exam the first 6 time he took it and is not well liked by the mostly anti-metahuman Lonestar. Oh, this will work!
The Meat:The beginning campaign had them solving a murder with a lot of corruption involving the courts and Lonestar and gangs. I basically threw together an LA Confidential story mixed with elements from 6 Blocks and the Gauntlet. Toss in tropes from assorted things like Lethal Weapon, Dirty Harry and every other cop/detective movie you've ever seen. It was glorious. It took about 9-10 sessions to play out. Along the way they were at ne point actually on the run themselves, trying to prove their own innocence. It ended dramatically with them bringing down judges, a few upper echelon Lonestar, a major drug dealer and being totally adored by the press and totally despised by their fellows for daring to cross the thin blue line.
At this point, I went to Gencon. And was one of the team of 6 that won that year, after years of trying!

The ironic thing? That year the Tourney had us playing ... law enforcement. I played a Marshal that was part of a multi-law enforcement taskforce created to bring down a terrorist.
I came home with a whole new plan (and a leather bound copy of SR4!) I would take these cops and retire them from Lonestar, give them new identities and recruit them for a special Marshal taskforce. They sort of became the Miami Vice/Mission Impossible/Anti-Runner task force. Impersonate runners to stop the bad guys and save the world. This task force was headed up by my Marshal character from the Tourney who effectively took over their "Johnson" role. I managed to play this for a couple years where they did everything from bust drug smugglers, uncover an AI creation plot, and saved Seattle from an anti-metahuman group planning on releasing a bio-toxin that targeted the genetic differences in orcs and to some extent trolls, lethal about 50 percent of the time. This campaign was only retired because I moved out of state.
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THE POINT OF ALL OFF THE ABOVESo, hopefully this history of my campaigns can give you some ideas of how you can make a "non-runner" game. Two of my most enjoyable campaigns were non-runners. One was playing gangers and one was playing cops who then became federal agents. One was based one what the group elected as a storyline and the other was structured by my own thoughts for a setting with input from the players. I think the key thing is soliciting your players input. Find out what kind of game they want to play. Let them know what kind of game YOU want to play and sell it! Be involved in making their characters. Don't hesitate to bribe them with little things in character creation if it helps steer them on the track of what you want to do with the game. You aren't going to break the game by allowing 5-10 BP worth of stuff here and there in character creation. But then be firm once the game has started.
In the cops game, i half created the characters and let them fill in all of the blanks. We negotiated here and there. I let them know i wanted the types of characters that were created but left the specifics up to them. If you are playing a themed game then everyone has to be on the same page. The trolls were easy, "Make a bad-assed troll go-ganger. Has to be a troll. Has to have a bike. Has to be a member of the gang." The cops wouldn't have been without cooperation from everyone, including myself. I think it also goes easier if your players trust you as a GM. They have to know that you aren't out to GET their characters and that you are as invested in a good story being told as they are in creating that story for you.
A final note: I have started each campaign with a variation of the classic Food Fight. I try to shake it up each time, but the elements of saving/destroying a Stuffer Shack while fighting with gangers is always at the core. The Original Campaign was traditional Food Fight (plotline taken from the SR2 version, i believe). With the Trolls they were the gangers shaking down the local Shack. In Denver, I threw a wiz gang at the PCs, heavy on magic combat. With The Marshals they were the cops and witness the event go down from a stake out on something else and get involve in a sort of Dirty Harry "Make my day" sort of deal. It's a nice tradition and one my players seemed to enjoy.

Good luck to you!
Vlad