Dammit, same here. Just sat down, logged in, entered the Omusomething system, and SERVER NOT RESPONDING on the "Loading..." screen. X'd out, tried to get back in, stuck at "Retrieving list of characters".
Seriously, Cryptic. Beta's one thing. You're basically LIVE now. Get your game on and stop screwing up everyone's first impression of STO.
It tends to get worse after launch. Just wait until the 2nd. Give 'em time.