Do you knot or not knot? I thought I'd clear up the mystery as to when knots are appropriate and when they're not. Ha, ha, ha! Okay, enough of the not, knot stuff!
With counted cross stitch, it's generally recommended that the thread tails be woven in behind the stitches on the back. Cross stitch fabric, esp. evenweaves and linens are thin so knots would show through on the front, giving the finished stitched piece a lumpy appearance.
With crazy quilting, I would say that it's a matter of personal choice. For the most part, I knot my threads. With the foundation fabric and all the various surface fabrics, any knots on the back will not show through on the front:

There is one exception to that in crazy quilting. With Silk Ribbon Embroidery, I weave the tails under stitches in the back. I used to knot them. But too many times, while working in other areas of the block, I'd catch that knot and end up pulling the Silk Ribbon, messing up my stitches on the front. It's best to weave those tails under other stitches.
With redwork and outline embroidery, lumps from knots
can show through on the front. The choice however, is really up to the stitcher. Most of the vintage embroidered pieces that I've seen at flea markets and antique shops have knots on the back. My own grandmother taught me to knot my threads so I will openly admit, that I knot when I do redwork and outline embroidery:

I hope you find this post helpful. Instead of just posting photos of my stitching, I've been trying to offer you helpful hints along the way.
If you like my Redwork Cat and would like to stitch him, you can find the patterns for him and his friends
here.