The key to this question is choosing a casinos with a good reputation. The vast majority of online casinos are honest and have solid, well-run operations. There are over 1000 online casinos on the internet. If you really want to play it safe then you are better off playing at casinos that have a been around for a while.
There are many internet casinos with good long-term reputations, that are well known in the industry. These casinos simply would not last if they didn't pay their players. There are many good advice sites on the internet to assist you. We spend a lot of time researching and playing online casinos. After years in the business, we know the industry and the people that run the sites. We only deal with organizations that we can trust. If you try online casinos that are not recommended then you increase your risk slightly.
I have personally never had any real problems collecting my winnings. As of April 2004, I have been paid over $69,000 US, made up of 90 different withdrawals from 49 different casinos. That is 100% of what I have withdrawn from the online casinos. I was a little worried about one casino, but I just got paid. In case you are wondering, the vast majority of these withdrawals were made before this site was created and I have not used any influence this site may have to ensure payment.
Unfortunately, there is no guarantee. I recommend that you keep good records of your deposits, the bonus expected and received. You should especially keep track of your withdrawals and the withdrawal dates. It can be easy to forget what you won weeks before.