I used to trade doges with Cryptsy, it has the highest volume but there are also other nice exchanges like Poloniex or bter which are a great deal.
the easiest and almost fastest way to trade doge is on bter.com.
I use bter.com just for a few coins (NXT, Doge, PPC) but I like very much their concept.
Poloniex is showing ssl error:
And not sure about Bter I read cpl of posts like this:
https://bitcointalk.org/index.php?topic=389591.0 and others.
Do I have to get verified at Cryptsy to withdraw my coins, I only want to deposit Doge and take out BTC?