You know you should make eye contact. You've read the articles, gotten the coaching, and even tried it out a few times. It's scary though. Especially with people you don't know. How much is too much? How much is not enough? How do you find balance between being a flitting butterfly which never lands on anyone and being the creepy guy who won't look away?
Eye contact is best when making a statement that brings your point into focus. You can tell stories without making much direct eye contact, because you are painting a picture, perhaps running dialogue, and acting out the scene. But when its time for the payoff line - deliver to one person. It will draw everyone else into the moment.
People you know. People who are smiling as you speak. People who fit the profile of what you're talking about at the moment (business person, young or elderly guest, corporate manager, etc.). Don't go to the same well too often, however - in fact, more than once every 10 minutes, or 3 times in an hour may give that person, and the audience, a genuine case of the willies. Be sensitive if people look away, and move your gaze quickly, perhaps to the person next to them.
Caveat - be careful about looking at family members. This can throw you off your game, particularly in emotional parts of your presentation.
All over the room. Spread out your individual eye contact to quadrants of the audience - forward, right/left, back. Even if you can't see someone, pick a spot where you assume they are, and speak to them. Making eye contact in one place vs. another too often may give your audience reason to wonder if you care more about, say, the execs at the head table more than the room as a whole.
If you have an obscenely large audience, you'll want to quadrant it out. If you feel like you are looking at a specific person in the upper deck, all 100 of them in the section you're looking at will believe it's them you're keying on.
Creepiness occurs quicker when a male speaker spends too long making eye contact with women in the audience, or even makes eye contact ONLY with women in the audience. The reverse does not appear to be true, though if a female speaker spends too much time looking at a male audience member, it can create an odd dynamic with other women in the room. Men looking at other men they do not know can create a level of tension, simply because it can instinctively feel like a challenge of sorts, whereas I've heard/witnessed little to no issues with women making eye contact with other women.
Connection and Trust. An audience will often tune out a speaker who is just pontificating on stage. Lack of eye contact makes the speaker appear as if they are more interested in giving the presentation than the audience they are giving it too. As young people, we are often directed to look at someone when we talked with them. This was a sign of respect and attention, but as we grew older, also took on a sense of caring and trust. In the United States, at least, lack of eye contact goes hand in hand with lies and deceit at worst, immaturity or spaciness at best.
You should always understand the culture you are speaking when out of the country, or even when dealing with diverse audiences. Direct eye contact can be considered rude, aggressive, or lascivious to various cultures, including Japanese, East Asian, Muslim, and Nigerian, among others. (source: Wikipedia)
What Not To Do
Do not look over the heads of your audience. Don't pick a spot in the room to rest your eyes, such as a plant or door. Do not stare at the clock. Do not watch the floor beneath you. Do not bury your eyes in your notes. Don't stare at your power point. And, no matter what, don't stare into the projector glare - you'll go blind!
Eye contact is one of the easiest ways to connect with your audience, and gauge audience reception. Done poorly, and you'll either become the addle-brained 'Dory' (of Finding Nemo fame), or the 'Must Look Away Medusa' of Public Speaking.
Done correctly, it will enhance your credibility and message retention, and you will be on your way to being the presenter who Speaks...& Delivers!