We were all disappointed by Microsoft's attempt at Shadowrun. Lets hope that doesn't sour the IP for a while.
That being said, here are 4 different ways of creating a Shadowrun game:
1. FPS set in the (real) Shadowrun world.
The world of Shadowrun is, IMO, more important than the rule-set. A single player FPS set in the world of shadowrun, telling an authentic shadowrun story could be a very good game. This is probably the weakest of the options,
1a. Rainbow Six (original) version of Shadowrun.
More of a variant of the FPS shooter style game, but while the FPS one focuses on telling a story (ala Halo) this one would focus more on the tactical planning side of doing runs. It would still be FPS, but would include a larger focus on planning out the runs over simply running and gunning.
2. Grand Theft Auto style Shadowrun
Probably the closest non-RPG style game we could get to a shadowrun game. The over-all set up of GTA would work for Shadowrun. Open world Sandbox, shady locations, people giving you missions, etc. Someone with good modding experience could probably put in a lot of work and mod up GTA 4 to be a shadowrun game. For this you can think of what would be a natural blending of the old Sega game with modern sandbox gaming.
3. Metal Gear style of Shadowrun
Another Action game version of shadowrun, this time the idea would be to use a set up similar to the "tactical stealth action" of the MGS series in a shadowrun world. The entire game may take place during a specific run.
4. "Mass Effect" Shadowrun
Here we start touching in on the Shadowrun world from an RPG stand point. Still rather action oriented, because I think shadowrun warants it. The system can be tweaked to fit all the different playstyles.
5. Shadowrun MMO
The holy grail of shadowrunning. An MMO sandboxy world with everyone playing shadowrunners of different ilk. The ability to hire on fellow runners to complete a mission, deal with the mega corps, etc.