I wash my organics (exceptions: when I'm lazy and in a hurry, I don't always wash the greens that are in packages and say they are triple washed). It's not to remove pesticides (which I wouldn't think would be totally 'removable' from non-organic produce anyway, because not only does the produce get sprayed with it, it 'drinks it up' from the water that it is irrigated with).
Another exception: if I pick them fresh from my garden or yard (wild stuff). If there's no visible poop on it (like from a bird) or dirt, I just eat it as is. If there's some dirt, I do a light rinse.
Lately, I've been spraying my non-home-grown produce with a 3% food-grade hydrogen peroxide solution (to kill any bacteria, which could be transfered to the food from other people touching it. I mean, who knows how many people have been handling it before me, and what they've been touching beforehand?).
I've also used a mix of white vinegar (sometimes with baking soda) and water. (white vinegar has been shown to kill bacteria as effectively as, if not moreso than, bleach). I soak non-organics, but just spray and wash the organics.
For mushrooms, I wonder about them as well, because they often seem to have dirt on them that is hard to get off. I don't eat them often (partly because of this problem), but when I do, I run water over them (but only over the top, as if they are umbrellas and the water is rain: don't let the water get in the 'gills' underneath) and wipe them with a paper towel. You can also take a damp paper towel and wipe them off.
I actually prefer getting dried mushrooms (and assume that they are cleaned well enough before drying, though soaking and rinsing them cleans them as well), in part because I can't always find organic fresh ones (and also because they don't seem to last long).