If you have not verified, and have no intention of verifying, expect to never see those coins again, Bittrex have stolen from me, holding my coins ransom until such time I legitamise a terrorist organisation masquerading as guberment, by begging them for some ID to share with those extortionists, which will never happen...
And they are ignoring my support tickets for over a week now...
Not wise depositing with them, if you have no ID and or wish to remain anonymous...
This is probably the best advice to start off with on any centralised exchange. In fact, only start depositing when you've achieved the highest possible verification. Firstly, you'll be somewhat safer from sudden account blockings (which they seem to frequently do to unverified or basic accounts), secondly, they will prioritise your support requests (and don't think you'll never need to open a support ticket).
I'm a Bittrex user, along with a couple of other similarly big exchanges, simply for the volume and opportunity to easily access alts.
But never believe for a moment your funds are safe there. If you don't want to use them to trade, withdraw and keep in your own wallet. Whatever funds I have on exchanges I am ready to lose - I've been lucky so far, but it's really only a matter of time before even the most reputable exchanges screw you over. Just Google Coinbase, the biggest and most reputable of them all. See how even the big "crypto personalities" are threatening action against them.
And yeah, Mt. Gox. Even angel investors weren't safe when they shuttered.