Depending on the yarn and the nature of the fabric you have knit (lace vs a very solid stitch) the results can vary a bit. If you have a slippery yarn you have to work harder at hiding the ends and I have even read of folks sewing the tails in with needle and thread. But wool yarn tends to stick to itself and it much easier to deal with.
I never tie knots and have never had anything fall apart. I have had the experience of ends popping through to the right side sometimes. When I work in tails I put them in seams sometimes dividing the yarn and working back on itself some. If it is not in a seam I like to do something called duplicate stitch to work in the ends. This works well in St st fabric. Here is a link that describes how to do it. LINK I have found that the ends will pop to the front using this technique, but it won't come undone. I have lately been leaving a bit of a tail 1/4-1/2" sticking out on the back side after doing this. I think this is going to keep them where they belong. It is a little unsightly but I'd rather have that (on a sweater not on an afghan or something where both sides will show) than ends popping out.
Wool yarn tends to felt to itself and make ends easier to hide. I'm making a wool sweater right now with stripes and lots of ends. I worked over ends as I went as much as I could and then have hidden some ends in seams or used duplicate stitch. On all the tails I have left ends sticking out and I'm hoping they will felt to the item with use and not stick out like they are doing right now. I have no worry that anything will come loose with washing though.