Betting a Draw for Deception
People like to take the path of least resistance, especially when money is involved. In poker, this translates to a person checking a draw. Afterall, why risk additional money on a hand that may or may not materialize? The answer is simple: Deception.
Some books say to bet your draws, some say to check and take a free card. Both strategies have legitimate reasoning behind them. Personally, I take a lot of mental notes when I play, and use my image to my advantage. Normally, I have a tight image. This means that people respect me when I bet, and think that I usually have the goods. If I bet, there is a reason. I like to play that image for awhile, then use it to my advantage. Consider this example from a 1/3 NL game where I felted my opponent (I will refrain from comments until after the hand is over):
I am in a mid position with:

There was a limper in an EP, so I limped, and so did six other people. There were 7 people who saw the flop.
Pot: $21

It is checked to me, I bet $20. Everybody folds except the guy to my immediate right, who calls. We are heads up.
Pot: $61
The turn is:

The guy to my right checks, I bet out $40. He raises to $115 ($75 more). I smooth call
River:

He bets $60.
I push all-in for $240. He is in agony, but finally calls. I show the nuts, and he shows pocket 66 for the bottom set on the flop.
The analysis on this hand is pretty straight-forward.
From a mid-position, I limped with a drawing hand. I flopped the nut-flush draw. Most people would check-call in this spot. However, check-calling is usually interpreted as a draw (which is more times than not - correct). The people at this table were smart enough to think about pot odds. They will all try to put you on a hand as well. This is where you must think on multiple levels. My thought process goes like this:
If I check and call, then my opponents will put me on a draw - probably the flush draw. If it hits, then I have less chance to get paid off.
If I bet, then people will give me less credit for the flush draw. If the flush hits, then I have a better chance of getting paid off. On times where I do bet, if I bet a little bit, people might see that as a “pot-sweetener” bet, and be less likely to pay me off with my flush. If I make a pot-sized bet, then they will think that I am trying to push out the flush-draws, and it is unlikely that they will put me on the flush if it hits.
These situations are where you have to put yourself in your opponents shoes and look at YOUR actions and how they come across. You should use these actions to manipulate the situation. I decided to make a strong pot-sized bet for deception - hoping to give the illusion that I was afraid of the flush draw. The turn gave me the flush.
My opponent checks to me, so I lead out again, but with a smaller bet - about 2/3 the size of the pot. I immediately get raised. What does this mean? The opponent probably had something on the flop - 2 pair, a set, or perhaps a flush-draw himself. The only 2-pair I can put him on is 86. A set of 8s or 6s are a reality, as is the flush draw. I have the nuts at the moment. The question is, do I raise right now and let the cat out of the bag, or do I play coy and smooth call? Raising big would let him know that I have the flush. He has about $200 more behind him, which I want to get into the pot. I doubt he would put it in at this point, so I just smooth call to make it look like I am afraid of the flush possibility.
The river is inconsequential. He leads out with a rather small bet of $60. A normal raise would be $180. Since I only have $240 total, an all-in push is correct. However, there is another reason why this push is even better. People will sometimes bluff all-in when they miss their draw. I push all-in and he goes into the tank. He even says, “I think you had a huge draw and missed it”. After about a minute, he calls, and I causally flip over the nuts. He shakes his head and says, “That was a very good smooth call on the turn. That is what committed me to the hand.”
The bottom line is that people will try to put you on a hand by your bets. While this is normally a good strategy, a smart player will use the situation to his or her advantage to manipulate the situation.