I've knitted a bunch of knots and links lately, principally in conjunction with the 2014 AMS Special Session my compatriot Carolyn Yackel and I organized. In particular, I developed a methodology for knitting many torus knots and torus links. (That will become a paper eventually. That is, there's a draft of it, and if you want it shoot me an email.)
Of course, torus knots and links are named so because they can be wrapped around a torus without crossings. And I like to knit tori from time to time. Here are a few torus knots knitted into their embedding tori (all public pages):
(5,3) torus knot embedded on a torus
(3,2) torus knot embedded on a torus with one chirality
(3,2) torus knot embedded on a torus with the other chirality
... and I have a triple braid for view on ravelry.