There have been rumors of BR [movie] sequels for years, but so far nothing has come of it. In one interview, BR director Ridley Scott once stated he would have made a sequel years ago, if only he had been given permission (since he himself doesn't own the movie rights).

Some years ago, there was talk of a script called "Blade Runner Down", which was reportedly based on Jeter's BR2 novel. The author of the script had the following to say about it:
"WB don't have sequel rights, only a first-look at making a sequel. The rights reside with original producer Bud Yorkin. When my script went out 'the town' loved it and offered me loads of jobs. Harrison's manager liked it but wouldn't give it to him unless a studio offer was behind it, and the only people in town who didn't 'get' my script were the majority of execs at WB and Bud Yorkin himself. What can I say? Other studios would love a crack, but it's these guys who hold all the cards right now. Harrison hasn't read my script and may never read it." - Stuart Hazeldine, author of the Blade Runner Down script. (18 March 1999).

For more (old) information regarding any plans for a sequel:
http://www.corona.bc.ca/films/directorscut/980308.html
http://www.corona.bc.ca/films/directorscut/980310.html
http://www.philipkdick.com/news/archive1.htm

Some other rumors told one of Scott's projects, Metropolis, could have been a disguised BR sequel. The project seems to have been shelved, anyhow.

There have been three *written* sequels, "BR 2 - The Edge of Human", "BR 3 - Replicant Night", and "BR 4 - Eye and Talon" (For more information on these, see the "Literature" section).