There are slight differences depending on the country of origin, but basically you can say: No, you can't.
Transfers are tracked relatively closely, partly because of the various money laundering guidelines that are in place worldwide (and therefore every transaction must be monitored...). Basically, however, government intervention is only worthwhile here for larger amounts. So if you deposit $10 on BC.Game, for example, it won't attract much attention. But if you regularly deposit $1,000, it certainly will.
Governments through bank system can trace money flow in bank transfers and apply many criteria for detecting suspicious bank accounts with too many transfers in and transfers out in numbers and also in total value. They can do their works and with time, they will filter very accurately bunches of accounts that looks suspicious enough. You know, this way, governments can break down underground systems for gambling operations in their nations. If it is illegal in their nation by law, they will take severe actions.
If you are simply a gambler, you will have less risk than people who cooperate with casions for affiliate money and more, but surely your bank account and you can be in troubles, just with less risk.