Removing hot break is beneficial to your finished beer. Many of the compounds taste bad and can stay in suspension through fermentation to packaging. Totally removing hot & cold break, such as with a pre-fermenter filter, can damage head retention. You need some of those proteins. Brewing Techniques has a good article on the subject.
There are a few methods of removing trub & break from your wort. You should weigh your time & effort against the benefits of each method.
Skimming
During the boil coagulated gums and proteins rise to the top in the first five minutes. Many homebrewers skim these off. Most pro brewers do not.
Kettle Screen
Using a coarse filter on the exit of your filter catches much of the hop material. I used a copper scrubbie on the tip of my racking cane and now have a stainless screen and bottom port on my kettle. This is an easy, mostly effective, way to leave break behind. Some pro & home brewers use this technique.
Whirlpool
At flame-out you create a whirlpool in the kettle (or other vessel). This piles the hop debris and hot break in the center of the vessel, allowing you to leave it behind by transferring from the side. Some homebrewers do it. Most pro brewers do.
It seems this is the best way to leave hot break behind. It is easy to do - especially with a whirlpool chiller (my next piece of equipment to build).
Hopback
A hopback is a chamber between the kettle and chiller. You fill it with hops and pass the hot wort through it to pick up aroma compounds that the boil would normally drive off. While not appropriate for most styles of beer, it is an effective filter.
Coolship
This is a long, wide, shallow open stainless or copper vessel. Hot wort rests in such a vessel for 1-3 hours to cool and settle. It is an old German technique, very prone to introducing infection.
Post-Fermentation
I find I can get clear beer by cold-conditioning my beer post-fermentation. Leaving the beer in the fermenter for longer is a tried and true method of clearing your beer. Here's a pic of my Classic American Pilsner.
My CAP is on the left, Lone Star is on the right.