Poloniex and etherdelta, they are the only ones who are not asking for a bunch of identifications before depositing money and closing the accounts.
Bittrex is a shit, dont even think about putting funds in there if you dont have an enhanced account, because you are going to get all your funds freezed, and if you put more than $1k in there without having an enhanced account, they are going to close your account because you were supposed to be trying to "launder money"
Criptopia is a good option to exchange without having your account verified too.
OP already post no talk about etherdelta and for others Poloniex has limit for withdrawal if you are not verified as some others also doing but still good are Live Hitbtc and binance if some one want to use without any verification but first read about limit this could be helpful for user