His four-volume history of modern times -- a trilogy on the "long nineteenth century", The Age of Revolution: 1789-1848 (1962), The Age of Capital: 1848-1875 (1975), The Age of Empire: 1874-1914 (1987) and a sequel, The Age of Extremes: A History of the World, 1914-1991 (1994) on the "short twentieth century" -- is really completely fabulous. My understanding is that it's out of date in a great many ways, but it's not only fabulously written, but is simply chock-full of historically interesting ideas. Sure, it has flaws and gaps, which means it needs to be supplemented. But then, no book is a good place to stop. These, however, are a good place to start (at least given basic high-school or college history: Hobsbawm tends to be writing about the meaning of events more than narrating them, although he does some of both). Among the more unmistakably brilliant of historians I've read.
Perhaps someone will come with proof-texts to disprove this (it's been a while), but one of my memories of those books is that -- unusually -- when Hobsbawm said something like "everyone" or "the world", he didn't meant Europe, or westerners, or anything like that -- he only said it when he meant, well, everyone, and that if he meant something less he said so.
Rest in peace.
Update: From the comments on this Crooked Timber thread on Hobsbawm (links added):
I notice that the obit in the Guardian is partly written by Dorothy Wedderburn (a sociologist of technology who sounds well worth knowing about), who herself died two weeks ago. Her obituary in the Guardian was by… Eric Hobsbawm. Of course these things are written far in advance, but it comes across quite oddly!I find that quite eerie, frankly. Also funny. But eerie.