MC Escher would be proud.
Moe·bi·us strip, n: A continuous one-sided surface that can be formed from a rectangular strip by rotating one end 180° and attaching it to the other end. (or by twisting while circular knitting)

This can be done with pretty much any yarn, on any size needle to make however big a mobius strip you want. The hard part is just getting the one twist (see the Saga of the Mobius Strip for my problems with that). I'll just give the pattern for what I did.

Finished Measurements

circumference 58" (147 cm), 6 1/2" (16.5 cm) wide
Materials

1 3 1/2 oz/100 g ball (each apporx. 142 yd/129 m) of Paton's Divine (acrylic/mohair) in #06006 Icicle White
1 size 13 (9mm) circular needle, approx. 24"(60 cm) long
stitch marker
darning needle

Gauge

10 sts and 14 rows to 4"(10cm) over Stockinette st (for circular knitting - knit all rows)

Directions

Cast on 125 sts.
Row 1: Make one twist (180 degrees, the front should become the back at the end of this row). Mark last stitch.
Row 2-30: Work even in Stockinette st.
Cast off. Weave in ends.