Well, we had a bit of a stumble with the Icon of the Month series last month. Somehow, I forgot to post one for April and by the time I remembered, it was just too late. It didn't seem quite fair to post one halfway into the month, so I opted to skip it. Fortunately, I did remember this month, so let's get on with it.
To me, though, Troi had a lot of potential that was just never utilized and developed. We saw glimpses of it with her empathetic powers coupled with her natural intuition and diplomatic skills. One dumb criticism I've seen of her is about her having her own seat on the bridge of the Enterprise when she was "just" a counselor. That ignores her aforementioned skills and abilities. After all, she was usually the one briefing Picard on whatever alien races they were going to meet during a diplomatic mission. She was also the one he turned to when he needed input on what someone or something was feeling during the various shenanigans the Enterprise found itself in. It's worth noting that in the Star Trek: Titan book series, this role she had on TNG is reflected in her position as Diplomatic Officer of the USS Titan.
Another critique is in her "lack" of piloting skills, that the two times she was shown at the helm of the Enterprise-D and E, she crashed them into either a planet or another ship. This is really incredibly stupid because it ignores the context of those two instances. With the former, the saucer section was caught in the explosion of the Enterprise-D's stardrive section (this happened in Star Trek: Generations, btw) and was sent crashing down to the nearby planet. If anything, Deanna turned the crash into a crash landing and saved everybody. In the case of the latter (Star Trek: Nemesis), she rammed the Enterprise-E into Shinzon's ship because Picard ordered her to.
In terms of favorite episodes of moments, one that comes to mind is Disaster. In this one, the Enterprise is hit by two quantum filaments and left severely damaged and disabled, with the cast being trapped in different parts of the ship. Troi finds herself in command of the bridge owing both to her rank as Lieutenant Commander and that the bridge officer that was in charge took an exploding control panel to the face. She's ultimately faced with two choices when it's discovered that the ship is losing antimatter containment and will blow up if it isn't fixed. Ensign Ro argues for a saucer separation because they have no idea if anybody in the stardrive is still alive and that it's better to save the people in the saucer than for everybody to die. O'Brien argues against this and Troi ultimately agrees with him, but at the end of the episode notes that Ro could just have easily been right.
Face of the Enemy, where she's kidnapped and forced to pose as a member of the Romulan Tal Shiar in order to help with the defection of a Romulan Viceproconsul and his two aides. It was interesting watching her take on the mentality of a Tal Shiar agent which is the polar opposite of her normal personality.
All in all, Deanna Troi is a character that could and should have been handled better by the writers, but still managed to be as memorable as any other Star Trek character, male or female.