From time to buy, I buy too many bananas. For the future, I am considering refrigerating them instead of eating them, but they turn black.
How can I know whether a black banana is still edible?
Open it up. If it's soft and pale brown or darker inside too, it's overripe and no longer good for eating straight; however, it can be used in baking, banana bread, or smoothies. Once it's black, the banana is garbage.
One thing to add to the answers above - as bananas ripen, the starch in the flesh is converted into sugar. This continues until the starch that was providing the firmness and structure for the banana has, for the most part, been converted to sugar, which is also partly why the insides continue to get mushier as the banana ripens. So more time converting starch to sugar means sweeter fruit.
This is why black bananas are often preferred for breads and such - when the peel has turned black, the banana has converted almost all the starch to sugar and thus has gotten as sweet as it can before it spoils.
So for the sweetest possible banana bread/shakes/smoothies/etc, let the banana peel turn completely black, but harvest the banana before the insides turn to dark brown or black since that will indicate that the flesh has spoiled.
For eating out of hand, check for a fermented, alcoholic kind of smell from the banana flesh. That's a good indication of too ripe. Those ones are generally still fine for cooking, though.
I totally agree with Caleb that I don't believe they ever really go bad. Of course, once they get moldy, you can maybe draw the line, but for my banana bread and cakes, I prefer to let them get completely and utterly black. I even deliberately wait for them to develop the banana liquor that gives such a depth and richness to my baked goods. After they get freckled, then turn black, then get a little shriveled, I put them into the fridge and after a little more time the sugars almost ferment - when they start to ooze their liquor you are good to go (and you can even smell a note of alcohol). I challenge you to try it for one batch of banana bread; it is wonderful.
I wouldn't eat a black banana. I do the same thing you do. I buy extra, and then I freeze them. When they are in the freezer they turn black, and then I make it into banana bread. Personally, I think the bread tastes better when you do it that way.
IMO, bananas never really go bad. If you can get past preconceived ideas of how they're supposed to look, you'll find the older they get the better they are. I just ate a blackened, mushy banana. It has been in my fridge, not freezer, for about two months. It tasted like buttery sweet caramel with a texture almost like ice cream or gelatto. For me, black, mushy bananas are a decadent, dairy-free alternative to ice cream. Dare you try it. Another favorite dairy-free dessert is grill-baked or oven-baked whole sweet potatoes in the skin. I make cross sectional slices not quite all the way through, down the length of the potatoes. Place each one on its own sheet of foil. Cover them with a little honey and cinnamon. Wrap them up and place them on the grill over matured coals. I put them on after I've done the meat. Then I just put the lid on the grill and forget about them till morning. That morning, I put them in the back of the fridge. They make an awesome dessert that evening.