One option is to stick with scarves but try a more complicated stitch pattern in the safety of your rectangle. There are some great stitches that create the effect of a woven fabric and almost don’t look like knitting which can be fun to play around with.
Or try a quirky, quick knit that's a variation on a traditional scarf (but still essentially a rectangle!).
Or try embellishing a plain scarf into something personal and unique - embroider a quote from a favourite book.
If you want to branch out from neckwarmers, try tackling another part of your body. Armwarmers or fingerless gloves are another good project as they’re much simpler than they look. You can either knit them in the round (and add another skill to your needle) or knit them in – you guessed it – a rectangle and simply sew up the side seams when you’re done. This led me to my first attempt at cables (not as scary as I thought) and it was a satisfyingly quick knit.
There's more to the humble rectangle than meets the eye....