Popularity is very important for a site for many reasons.

Trust - The more that people have used and know people that have used a site, the more likely they are to trust that site.

Search engines - The more popular a site is, the more useful it will be to a web surfer and the more reasons for search engines to return the most popular sites

Life-span - The more popular a site is, the higher the possibility that it will continue for a few more years.

The question is "How do you judge a sites popularity?".

Links - For a few years, search engines ranked the popularity of a site on the number of other sites that are linking to it. The problem with this is that people are now engaging in reciprocal linking and link-spam that reduces the effectiveness of this.

Traffic - It is often though that the more visitors or traffic a site receives, the more popular it is. The problem with ranking a sites popularity on traffic is that pop-up advertising and other devious methods can take a user to a site on loading another site. This means that although a site may receive more visitors or traffic, it may not be popular in the true sense of the word:

1. Widely liked or appreciated: a popular resort.
2. Liked by acquaintances; sought after for company: "Beware of over-great pleasure in being popular or even beloved" (Margaret Fuller).

The best way to judge a site popularity at the moment is by using a search engine like Alexa, Google or Yahoo