I leave unsalted butter out all the time in a covered dish. I use it frequently and it never goes bad. Put it in the fridge when you know you won't be using it for a few days. And be sure to wash the dish before refilling.

I find that if I leave butter out it does not go "bad", but it does develop a stronger taste and smell. The smell is sort of oaky. Olive oil left uncovered and exposed to oxygen seems to do the same thing.

I typically take the butter out of the fridge first thing, early in the morning - and it sits (covered) on the counter until I put it back in the fridge that night, whenever food is done for the day. Wash, rinse, repeat. In hot weather - if the dreaded AC isn't blasting, turning the entire house into a meat locker - I tend to keep it in the fridge and just take it out a half hour or so before using it.

At room temp, butter spreads better and I think it tastes better too - few things are full flavored when ice cold. The French have this one right - they neither refrigerate butter, nor slather it on their bread regardless of what they're eating: for breakfast, yes; alongside, e.g., a bowl of bouillabaisse, no.

The French have always left it out and they are still here. It tastes better.

If you're a frequent butter user, wrapped room temp (around 65 degrees F) butter is fine for a few days. Butter bells are great for soft spreadable butter.

I've never had room temp butter go bad. Ever.

If you're not a frequent butter user, keep it in the fridge and just take out what you need a few hours before you'll use it.

Ahh..here's a bit on "Butter Bells" in video from the food network.
I just use a normal butter dish. Pewter..left out at room temp with 1/2 stick of butter in it for spreadable goodness on toast in the mornings. The butter bell/crock. Has some drawbacks...as you should change the water every few days..and in hot rooms. The butter can slide out into the water if it's not packed correctly. These have been used for hundreds of years.

http://www.butterbell.com/foodnetwork_video.html

Butter is perfectly fine let out of several days at room temp. It won't get bacteria in a butter dish left out covered.

Butter Bells..or Butter Crocks are common items in some places. These keep butter at room temp but seal the butter in a shallow pool of water. Butter can last weeks or more in those. Why do this? Because when you want toast in the morning..nothing is worse that butter that's hard and destroys the toast.
http://www.butterbell.com/

salted butter should be okay for a couple of days at room temp. Unsalted butter goes rancid pretty quickly - not a bacterial issue, but a chemical change. Tastes nasty but won't really hurt you.

salted butter is the key.
salted butter can stand up to the attack of bacteria that will make it sour.
unsalted butter will get a bright fruity taste that will fade to a rotton milk taste very quickly without cooler temperatures.
Cultured butters, european butter also seems to fair better as well. with out the cooler.

I'm curious, too, of what folks think. My husband and I have a silent battle in the kitchen over this. He likes to leave it out. I'm in the medical field and the thought of all the bacteria grosses me out. I'm constantly putting it back in the fridge.