I used to try to avoid transferring hot break, as several times I've heard Jamil Zainasheff saying that it could have a flavor impact. However, I just don't have the ability to strain out hot break- those pieces are small! Since I have a counter-flow chiller, all of the cold break goes into the fermenter.
The only time I make an extra effort to avoid transferring trub is when I'm making a light lager. I still don't have trub free wort (again, since I have a CFC, I can't avoid cold break anyway), but I make an effort to avoid transferring straight out sludge.
I haven't noticed a difference in the taste in the final beer betweein strained wort vs. non-strained wort.