The following exchanges do provide the ability to trade without ID verification, but obviously as long as you stay away from anything related to fiat.
WEX
HitBTC
Bit-z
There are some more, but aren't really pushing that much volumes. I however would advice anyone to carefully consider that there are a large number of complaints against these exchanges.
Binance is the largest and most popular one, and has listed an insane number of coins, why do you still need other exchanges to be listed? Are you compiling a list or what? If so check for yourself
here.
And btw, it's not allowed to display referral codes like that.
Thank you, @BitHodler! I removed the referral code. Thanks for telling me!
Binance is, indeed, a wonderful option.
I asked for alternatives because a friend said, that her browser could not open certain exchanges' websites.
Maybe, I will write a list from the alternatives. If I do so, I will remember your help.