Counselor Troi was an useless crewmember. Her only task there was stating obvious. She is good at sensing wrath in a furious Klingon, who is swearing and destroying furniture at the moment. But she became better, when she got rid of the revealing dresses and enormous wigs, and started to wear a regular Starfleet uniform. It was not only her clothing, but the character itself changed too.
But the most annoying character from the world of Star Trek is Will Riker. He's disgusting and I hate him. Earlier shaved 'Baby-face Riker was quite okay though.
Lwaxana Troi...I didn't like her on TNG- she appeared there too much frequently. On DS9 she seemed to me quite better. I was quite surprised, that
I must say, I am much more into TOS and DS9, than TNG. I have a TNG avatar though, cos Conspiracy is EPIC.