While not significant crossovers, ER and Chicago Hope often referenced each other, most notably when both shows accidentally opted to use NASA's "Surgeons in Space" program as a plotline, in virtually the same week.
ER's Dr. Green (Anthony Edwards) and CH's Dr. Austin (Christine Lahti) both signed up for the program. Once the producers/writers realized they'd come up with virtually the same story line, they played with it. A lot. There were several episodes where these characters would talk about one another as competing for the same position. There was even talk of doing an actual crossover, and maybe even a jointly produced TV movie of both of them being selected and going into space, but the networks involved couldn't come to an agreement, and both shows dropped the storyline.
Chicago Hope also acknowledged St Elsewhere in an episode featuring Mark Harmon, who was on both shows as totally different characters. The setting was a medical convention in Las Vegas, and in one scene Harmon steps out of his hotel, under one of those animated Hotel signs. This sign was welcoming the attendees from the various hospitals, and as Harmon exits the hotel, the sign changes to read "Las Vegas welcomes the Doctors of St Eligius Hospital".