What is a double spend?
As someone who uses Bitcoin, what do I need to know about how the Bitcoin system prevents double spends? Are there still circumstances where they can occur?
A double spend is an attack where the given set of coins is spent in more than one transaction. There are a couple main ways to perform a double spend:
To prevent damages from the first attack - wait for one confirmation to appear on a given transaction. To prevent damage from the second attack - wait for 6 confirmations to appear on a transaction, or less if the transaction is small (but still require at least 1). Damage from the third attack can cripple the entire Bitcoin network, so don't worry about it - your business most likely won't be the main target (it's unlikely to happen without really big money getting involved).
For more information about all those attacks, you can check out my master thesis on Bitcoin security.
As a merchant, you can reduce the likelihood of losses from a race attack double spend by having your node properly configured (no incoming transactions, explicit outgoing connections to well-connected nodes). There still is a tiny risk of getting cheated even with this configuration but it is rare and relatively random. Thus the disincentive to the attacker is that if success in double spending only rarely occurs, each failed attempt is a profitable sale to the merchant and thus in the long run it is unprofitable for the attacker and profitable for the merchant.
There are circumstances where a merchant is more vulnerable. An unattended coin change machine at a laundromat, for instance, would be the worst case scenario for the merchant. The attacker loses nothing for failed attempts (presuming the machine is not taking any profit from each "sale"), takes the gains on the occasional successful attempt, and is not likely to get caught for committing fraud as by the time the laundromat operator is aware anything happened the thief is long gone. (Of course, countering this is the likelihood that blockchain monitoring would have identified the numerous double spend attempts and thus the laundromat operator can prevent even this from occurring.)
The Finney attack also has costs that make it less of a threat than it would seem. Holding a block costs about a dollar a second. So if once a block is mined but not broadcast and it then takes the thief forty seconds to complete the transaction with the merchant, there had better be a lot more than $40 worth of profit from doing so otherwise the attempt ends up being uneconomical over the long run. Again, the merchant would know eventually that the double spend had occurred (measured in seconds, if monitoring the blockchain), so this doesn't work well in circumstances where the thief risks getting caught. So the prevention for this is to simply not make large value transactions (e.g., hundred dollars or more) on 0/unconfirmed without some delay where you are watching for double spending.
The 51% attack that would reverse confirmed transactions is so expensive and thus such a remote chance of it occurring, it is not even of concern for a typical merchant. (i.e., someone spending millions of dollars to double spend using this attack vector, if it ever happens, is going to go after trades where large exchanges of value which occur -- think gold bullion traded for bitcoins under a bridge at midnight. They are not trying to buy your consumer electronics that you ship out via UPS nor are they meeting you at Starbucks hoping to defraud you of your $200.)
If everyone could spend the same Bitcoin twice, then the whole system would collapse because Bitcoins would not be scarce.