You didn't mention the country but there is Kraken that don't require any ID verification but you need to provide those info in your account profile.
Tier 1 - you can deposit and withdraw in digital currency only. Trading, however, is enabled in digital as well as fiat currencies. Full name, date of birth, country and phone number are required.
Then you have Liqui.io that also don't require ID either but they don't support much coins as Poloniex or Bittrex.
I didn't mention country because its part of ID proof.
Wow! good to know that Kraken let you convert coins to fiat and sit with them until you decide to buy some other coins. Do you know any other good exchange which like Kraken let you convert in fiat and let you trade with coins later?
They must not be letting you withdraw fiat without ID proof though I am interested in digital currency withdrawal only.