Well what does fermented apple juice taste like? Is it very strong? Does it taste at all similar to apple juice? 
Yes it can be verrrry strong. It tastes like the apple version of beer but more like wine, kinda.
It’s yummy. It isn’t all that hard to find, and not really more expensive than beer. Go to anyplace that sells a wide variety of beers (I go to my friendly neighborhood upscale wine-and-beer store), or to an Irish bar, and you can try it. I prefer it to beer, in general.
Over here (UK), Cider IS fermented apple juice - apple juice is apple juice, which had me confused when Americans referred to cider and small kids drinking it.
One step further, try Calvados if you can get hold of it - ‘brandy’ made from apples. Begian, if memory serves.
As with beer, you can get fizzy sugary rubbish which claims to be cider, or outstandingly-good stuff. And as with beer or lager, there’s a huge variety of tastes within the worthy produce, from extremely crisp & dry, through to rich, almost earthy flavours. But watch out, some of the bottled stuff is very strong indeed (8 or 9% alcohol isn’t unusual).
Also, look out for perry - like cider, but made from pears.
It depends. “Hard” cider – sweet cider that fermented after you bought it – is usually awful.
Commercial hard cider is more like apple wine. There are also variations in the flavor. Woodchuck (my favorite) is just slightly sweet. Hornsby’s is drier. There was one brand – Apple John’s or something – that had no apple flavor at all.
There are some apple wines that taste much like grape wines. The North River Winery in Vermont makes some nice varieties.
Calvados is from Normandy (which produce a lot of cider, too, by the way, “hard” cider, that is).
As for the taste of cider, I couldn’t tell. I like it a lot, but how do you describe a taste? It’s not like apple juice, nor like beer, nor like wine…
I think that’s not a common way to use that term. Most of the time I’ve seen “hard” cider only used to describe intentionally-fermented product. You might as well call the accidentally-fermented stuff “spoiled”, as if it doesn’t taste good, it probably was fermented by a wild yeast that’s not quite right for the job.
Ironically, I just bought my first hard cider last week, Hornsby’s , and it really is good. To me it tastes like beer and apple cider combined.
'Tis called scrumpy in its British homeland, and it tastes the same going down as it does coming up. Most bars don’t sell it, and those that do have special arrangements, like only selling it in half-pint measures in plastic glasses. It may have little chunks of apple floating around in it in its unadulterated form.
An elderly uncle of mine used to make his own cider. The bottle would have a thick layer of sediment on the bottom, and you could taste the orchard sweepings, slugs, and maybe the odd dead rat. And your breath the next day could strip wallpaper. Effective though.
Homebrewer checking in:
Hard ciders generally do not retain much of their original fruit flavor although you can have them ferment out sweet so you get something with hints of the original flavor. A few peel shavings added at bottling might help as well.
There is a company called Wyders that makes bottled hard ciders that many grocery stores carry. I love the pear one myself.
For about a $50 investment in buckets and such you can make your own hard cider type concoction for a couple dollars a gallon, watch for sales on a fruit juice that you want to ferment and buy a few gallons. Add some honey , little mead yeast (cuz we want alcohol content :D) and wait patiently for results. Many bars will also happily sell you their returnable beer bottles for a little more than the return value (these can be recapped with inexpensive capping tools) I used to pay $3 per case and any given bottle was refilled several times in its lifetime.
If you want to give it a try, look for Charlie Papazian, his books are pretty much the homebrewing canon.