Bladerunner and Johnny Mnemonic are excellent choices. Also, Hackers, while clearly being dated, is a good example of a shadowrun.
Some other good choices:
Lawnmower Man 1&2 - Corp does an experiment on a mentally challenged man, and turns him into a virutal god. A vengeful virtual god.
Ghost in the Shell - If I have to explain, you need to watch it.
Akira - Barrens living at its finest. Oh yeah, and you also have people with strange powers blowing up the joint.
S-cry-ed - Another anti-establishment themed anime, dealing with people who have powers called 'Alters' and the government that wants to control them for its own ends.
The Italian Job - If that isn't a Shadowrun, I don't know what is.
Ocean's Eleven - Another brilliant example.
The Sting - Old school long con. And damn good movie to boot.
License to Kill - Of all the Bond movies, this one is the most like a shadowrun, as Bond goes on a mission of revenge to get the person who tried to kill his friend.