I guess you meant within the context of "writing resources"? Because I have never bought a new dictionary, atlas or encyclopaedia since I bought an internet connected computer in 2000. With exceptions, online resources are generally more up to date and more comprehensive. I still have a dictionary, thesaurus, atlas and encyclopaedia, but never use them.
Obviously, you do need to be more careful with accuracy by only using credible and reputable online sources, but without mentioning them by name the big players in internet searches and maps fit that bill, and their are plenty of academic sources and published dictionaries that are now online. Even the most popular online encyclopaedia is ditching its reputation for inaccuracy, although I would always check the sources of any information given there. For dictionaries there are also urban dictionaries of slang and translation facilities that if in a traditional published dictionary would require several book shelves to hold them.
On the other hand, for a writer, there will be published works, still in copyright, that cannot be found online. They may want to quote or reference those and will need a printed copy of the work. For me, any vital, required reference books would similarly be those containing materials that I am unable to find online. Even for my local history, family history and genealogical research, the amount of records and materials that are now digitised is astounding. I could never have a library that large. The only reference book that I would recommend would be The Oxford companion to Local and Family History. Obviously, there are still many historical documents that are not digitised. I expect that in some niche hobby areas or niche subjects then there also must still be information that has not yet been digitised, and where a particular revered reference book is still the only place to find that information, but the ability to search and cross-reference with links makes any online source far more useful than a book or a filling cabinet.
However, there still are reference books that I do consider absolutely essential. These would be animal and plant ID guides and maps. When outside without WiFi and with limited mobile phone reception these come into their own and I ways carry my bird and insect ID charts when out walking. I would strongly suggest never relying solely of technology when walking too. Online maps and GPS gadgets are wonderful, but when you lose signal and dense fog descends all around you, you will wish you had a compass and a paper map with you. The only other reference books that I ever buy or carry with me would be tourist Travel Guides and The CAMRA Good Beer Guide.
Of course, on a desert island, I'd still need all of the above.
And I meant specifically physical books. (Or at least discrete e-books and not the internet generally.)
