Removing the flavour of smoke
There are a couple of specific cases where you may have some luck rescuing a portion of the dish.  THis is not removing the burned flavor, but rather removing the unburned portion:


For a large pot of something like chili or spaghetti sauce, if you realize it is burned on the bottom, you may be able to scoop off the unburned portion at the surface.  Don't stir and don't scrape the bottom.  You want to leave the burned portion on the bottom of the pan.

It still won't be as good as unburned, as some of the flavors will penetrate, but it may not be totally horrible.  
For a large cut of meat, like a roast, you may be able to cut off the burned portion, and rescue the remainder.


However, in general, once something is burned, the smoke and acrid flavors will penetrate it pretty thoroughly and there is no real way to remove that.  Masking the flavor with additional spices would be extremely difficult, and almost certainly require an unacceptably large quantity of spice (unless you are a fan of Dave's Insanity Sauce, in which case you may not care). 

You have to decide if the food is unpalatable enough that you just have to discard it.