I know that some of the people who are "popular" are also not well respected. I am thinking of one coworker in particular who is rather popular (has people stopping by his cubicle all the time and so on), but people make fun of him behind his back for being dumber than a brick wall and semi-useless at his job.
My answer depends on what is meant by "liked". I think that either one of respect or popularity on its own is relatively worthless. We should distinguish genuine friendship from both of these. As I see it, although it's possible to respect (part of?) someone who you do not like, the converse does not hold. You cannot truly like someone you don't respect. That is, respect is essential to genuine friendship. On the other hand, "popularity" - understood as sheer quantity of time spent socializing - seems far less important.
But my opinions should probably be taken with a pinch of salt. After all, I'm extremely introverted. I actually don't like being surrounded by people all the time (it's nothing personal, I just find social settings awfully draining). So I'd be curious to hear what more, er... normal... people think of this question.
P.S. I absolutely cannot recommend the Jonathan Rauch article enough. It's very funny, and also helps correct some common misconceptions about introversion. Do read it.