Ulqiorra is a sociopath devoted to Aizen and trying to understand the utterly alien concept of "Heart".
...Aaand that's pretty much it, aside from Segunda Etapa that came out of nowhere.
I can't understand the people who saw him as redeemable. Did we watch/read the same story? He spends litteraly more time psychologically torturing Ichigo and Orihime than he does fighting. And he does a whole lot of fighting.
Yes, his design was cool. And it's telling of his effectiveness when Orihime, despite having grown a backbone, is reduced to calling out for "Kurosaki-kun" after the mental torture he pulled her through.
He is the most overrated Espada with Grimmjow, really. I'd say only Grimmjow, Zommari and Yammy - and maybe Aaroniero and Nnoitra - are less interesting than him. The top 3 and Szayel leave him in the dust when it comes to actual personality, interesting abilities, backstories and "what could have been"s.
He isn't a bad character per se, just a rather cliché sociopath with a cool design. He just isn't as great as people would want you to believe.