I find that it depends upon the tie.
Unsurprisingly, knit ties look great with a button-down collar shirt, as do wool ties. However, I also find that as long as silk ties are a bit more casual, then they typically look good with an oxford cloth, button-down collar shirt.
As an example, the two ties on the left in this photo here (from a post of mine some months back) look great with OCBD shirts.
However, I think that some silk print ties can also look good - see here.
Then, of course, a knit tie almost always looks great - see here, here and here.