Here in New Zealand, people don’t go “to the hospital,” they go “to hospital.” And they aren’t “in the hospital,” they’re “in hospital.”
I’ve done a little digging, and it seems that for some nouns that denote “institutions,” the definite article can be dropped in British English.
The phrase “at table” – which is still occasionally used in American English – jumped to mind. But then other phrases, too – like at sea, in college, in prison, etc. It’s strange to my American ears to hear that someone is “in hospital,” but when taken in the context of the development of the rest of the language, I guess it’s not at odd as it first seems.