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It's tricky semantics, but from a certain point of view, Stargate does beat Dr. Who.
Remember that, what we in America call a "season" is called a "series" in Britain. According to the BBC, the fourth series of the new Dr. Who is going to start up around this Christmas.
So, if each "season" of Dr. Who is in fact a separate series, then Dr. Who is not one consecutive series, but 20-some-odd smaller ones.