I know that Stephen King talks about grammar and spelling as being in a writer's tool box, and I'm not saying they aren't there, but I just wanted to discuss the basic/actual/physical tools that I use when writing.
I like to write everything down first, on paper, before committing it to the computer. I do sit down and work on the computer as well, but I feel like it's easier to get out the story by writing instead of typing (I'm not sure why). After things are written down, they have to be typed up anyways, so it's kind of redundant, but it allows me to have an initial edit as I'm cleaning up with writing from the notebook as I'm typing it onto the computer.
While water will destroy ink on paper, ink won't fade like pencil. If you write a story in pencil prepare not to be able to read those pages 10 years later.
I also like to find the most frictionless pens I can, as I want to write fast. Cheap pens tend to write slower (you can feel the pen drag across the paper), although I have found nice pens at the dollar store before.
Gel pens are great. Felt pens are perfection, but the writing on the page can be thick and hard to read and felt pen ink is destroyed by water a lot easier than regular ink (in my experience) and these are very expensive.
These are also great for when you're supposed to be writing but you're doodling on the edges of your paper instead.
This is not a picture of my music, but I felt like it was applicable when discussing the wide range of music needed, at least for me, when writing.
I can write in complete silence, but I also like particular tunes to help set the mood for a scene (not in a gross way) or to help my imagination wander.
Last but not least, my netbook. I have a laptop but since the screen died, it has become essentially a desk top. To replace this computer, I had to find something a little more mobile, so I purchased a netbook.
Netbooks are not very good for many things the usual person wants to do with a computer such as viewing websites, downloading programs, doing anything that requires a screen that is larger than 5" by 8" (random guess); but it works for typing up documents.
My netbook (I actually own the same acer as pictured here), while aggravating at times, has become essential not just for my writing but also for my school work. It doesn't come with a disk drive, so you have to come into the 21st century and purchase a flash drive if you are going to use this with your writing and hope to transfer information to another computer. Or you can always email yourself documents, if you have Internet in your home (unlike me).
Not including my brain (which is pretty essential to writing), I think this is a complete list of the things I need and use in my own writing. Please feel free to share any tools that are unique to you and your writing in the comments area. :)