A fantastic addition to the famous pantheon of scarfs that Tom Baker sported would be this TARDIS scarf by Kate Atherley, tech editor at Knitty, a site dedicated to helping witty little knitters expand on their skills. Explaining the origins of the scarf Atherley explains:

"When I was a teenager, I insisted my mother knit me a Doctor Who scarf. Although the colors weren’t precisely right, it was exactly what I wanted: an absurdly long, multicolored scarf with a generous fringe. I wore it for years. And years. I was still wearing it when I finished university and started my first proper job.

"One cold winter day, a coworker made a comment in passing. I am certain he meant it to be helpful advice, but it stung more than he could know. He said that the scarf was childish, and if I wanted to be taken seriously in my career I needed to dress the part. The scarf got put away, and I spent more than 10 years dressing conservatively for a career that I never quite fit into. 

"Fast forward to 2005, when Doctor Who was relaunched to much acclaim, and I was busy reinventing myself and finding a career I could fit comfortably into. I never forgot my beloved Doctor Who scarf – I’d kept it all along – and I harbored a fantasy of reinventing it for my new life."

 Instructions on how to knit your own copy are found at Knitty