The usual suspects
Obviously a computer is the number one accessory you need on your desk when you're a writer. Add internet connection when you're a blogger … or in need to look up vocabulary when MS Word is making strange suggestions.
Even if you do most of your writing on a computer, pens or pencils and of course paper are another accessory you need on your desk. No one jots down a few notes on their computer. Besides, it all started out with paper once, or rather with chisel and stone.
This accessory is almost as important as the computer. When you spend hours or days, depending on what you write, you will at some point need to print it out to edit it or, in some cases, ritually burn the outcome of your creativity.
The unusual suspects
A writer needs fuel, like coffee or tea or whiskey. And a nice sized heavy mug is just the thing you need to fill with your liquid of choice to keep that engine going. Needless to say that a mug is THE must-have accessory for any writer.
It doesn't necessarily have to be a shirt. You could just as well go for pajamas or any other garment which gets you in the mood for writing. Slip on your writer socks if you like. It's like the lucky underwear of an athlete, even though you should wash it more often than they do. While not the most obvious accessory, it is one you shouldn't underestimate. The Muse might decide not to kiss you if you're not wearing your come-hither shirt, socks, or whatever.
This can be any book that has a meaning to you. Have it close by when you're writing. It's motivation and stimulation and usually proves very helpful when writer's block is setting in too.