I liked Q because he could say things that no other character on the show could say. TNG had an almost pompous air about it, everything was so very serious, but Q could come in and burst that bubble.
I get the feeling that was the whole point of the character. He was basically a foil to the stuffiness of the characters. That's particularly seen in the episodes where Picard defends their way of life, never thinking that perhaps Q had some good points. I mean, from our perspective, 24th Century Star Trek humanity has evolved tremendously in a moral sense. But how would that look to the Q, who have evolved so far ahead that they are basically gods. Humans must still look like apes to them in comparison.
And yes, I loved the character, he's my second favorite to Data.