As far as anime/Manga and movies to give people the feel of shadowrun, here's my list (some may have been already mentioned). Note, these aren't all direct lead-ins to Shadowrun, but they do display some of the mindset of people/corps, or give a good analogy for certain aspects of the Sixth World (like the Matrix).
Ghost in the Shell (including Stand Alone Complex)
Black Lagoon
Blade Runner
Johnny Mnemonic
Lawnmower Man
Hackers
Oceans' Eleven
Sneakers
Gone in Sixty Seconds
The Maltese Falcon
Road to Perdition