The most interesting people on Twitter are the ones whom you see and are amazed by. Although it is a common question to all, finding interesting people on Twitter is something that "depends on you", someone that seems interesting to me might not seem the same to you. So, first of all, you need to figure out what your interests are and what topics make you pay attention. Then it's just a matter of typing that topic on Twitter search and checking out users who are talking about the topic. That said, it is not always straightforward or  easy to find interesting users just by searching for a particular topic as you don't always get relevant results. In such cases, a better approach would be to take a look at sites which list users as per their power, grade and authority on Twitter.

FavStar

Get list of all time most Favorited tweets and choose to follow people accordingly. You can also sign in with Twitter to create your own list. You can either choose to follow all the people on a list or take a look at each person's timeline to make sure that they seem interesting to you and that you'd like to have a conversation with them.

TweetGrader

You can enter your country's name and get a list of most elite users out there. TweetGrader has its own unique algorithm that grades users as per different factors such as number of followers, power of followers, updates, update recency, follower/following ratio, and engagement. You can also have yourself graded on TweetGrader.

Listorious

Listorious surfaces people based on twitter lists.  Select a tag, for example, entertainment and it'll show users who have been listed the most by  Twitter users on their personal list. If tens of thousands of people list someone, then its worth taking a look, right?

Twibes

With Twibes, you can search on a keyword or browse  categories and find Twitter people who are interested in the same things as you.  Instead of searching for some topic on Twitter and finding irrelevant tweets, you can join a particular group of your interest on Twibes and converse with members who share the same passion as yours. That way, you won't ever get to read irrelevant tweets and can always follow conversations without any trouble.

Wefollow

WeFollow is a twitter directory which lists some of the most influencing and popular Twitter users in different categories.

Tweepz

Enter a particular keyword, name or location and get a list of relevant Twitter users. You can use name:, bio: and location: to specify your search.