Finding a full campaign is rare. Single adventure are easier to come by.
There are some adventures on the official Shadowrun web site. See "Adventures"
linkThe only full campaign I know of online is the Shadowrun Missions campaign. The first two "adventures" are online at the Shadowrun Missions
home page. See "Download Shadowrun Missions". This campaign is under development, and at least two more adventures in the campaign are almost ready for release.
This campaign, Shadowrun Missions (SRM), does not intend to produce enough adventures to keep a weekly game supplied, but rather to provide a world-wide campaign for conventions where players can build a character within the campaign over time, and run them at multiple conventions. There is a Dumpshock Forum for SRM.
link. If you want to use the framework of the SRM campaign for your own home campaign, that's fine. However, an character in your home campaign that has earned obtained Karma, Nuyen, or Gear from non-SRM adventures could not be played at a convention SRM game.