Now we finally know how Prometheus connects with Ridley Scott's original Alien movie, but does it also have ties to Scott's Blade Runner? A feature in the Prometheus Steelbook Blu-Ray suggests a connection between Prometheus' Weyland Industries and Blade Runner's Tyrell Corporation.
Redditor Huxleyism found this entry from Peter Weyland's journal in the Blu-Ray bonus features, indicating that, in his youth, Weyland knew Dr. Eldon Tyrell and that the two debated the use of biological replicants vs. mechanical androids. Although this may well be just a geeky little Easter egg rather than a serious narrative link, it actually fits with the Weyland corporate timeline. Blade Runner was set in 2019, and Weyland didn't receive his patent on cybernetic individuals until 2023. So perhaps Weyland's cybernetic robots came to replace Tyrell's replicants.
Given that a Blade Runner sequel is in the works, hopefully any future connections between the two universes will be in background references rather than in the narrative. We love Alien and we love Blade Runner, but there's no need to cobble the universes together.