This is a question that Sellers and Buyers will have very different answers on. Let's focus mostly on the Buyer, and the Seller's point of view will be covered in the process. First, I want to start off with a question. Is a deposit required when making an offer?
Now I am not a lawyer, but from all the legal information I have seen, the answer is that no, a deposit is not required. A promise to sell and a promise to buy are valid consideration; consideration being something of value that is required to make a contract valid.
So, the reason to put a deposit down with an offer is to show good faith. The seller is effectively removing their property from the market while you decide whether or not you are going to buy the property. That's right, normally the buyer gets a chance to decide if they want the property (actually if they "can" buy the property) because most buyers make their offers conditional upon something happening. Some of the most common conditions are financing, inspection, review of leases, environmental assessments, and on and on. If the buyer can not satisfy their conditions, their deposit is returned in full and both parties go their separate ways.
   There is one small problem, though. If a seller feels the buyer didn't make a real effort to satisfy their conditions, they can demand that the buyer prove that they "acted in good faith" and made a "reasonable effort" to satisfy their conditions. For this reason, the initial deposit is usually quite small so that the buyer is only risking a small amount (In reality sellers have proven highly unlikely to pursue this route, but it can happen).
    Gerald, did you say "initial" deposit? That's right, many offers have a second deposit that the buyer pays after they remove all their conditions. Since the conditions are removed, the money is at very little risk because the buyer should have done their due diligence and have found that they can indeed purchase the property. Basically, the buyer is unconditionally agreeing to make the purchase.
    I often suggest my buyers make their second deposit a large one. This has the psychological effect of making the offer look better, and the buyer look more serious. This can sometimes lead to the seller being more reasonable in their negotiations with the buyer.