There are many facets to Bitcoin's security. One of those is the protection against double spending. The way Bitcoin prevents this from happening is by using a confirmation system. Once your transaction has been added to a block, each additional block generated on top of it decreases the chance that you can double spend the coins from this transaction. Six additional blocks is considered quite safe, though as a receiver you could choose to acknowledge payment earlier. Since the network generates one block every ten minutes on average, six blocks is about an hour. This is probably what you are experiencing.
In short, don't worry. This is by design, is one of the core security mechanisms of the currency, and is one of the trade offs for using a decentralized system. If you use MyBitcoin (or some other future Bitcoin aggregator), transactions between members are instant, as they are not written to the block chain. The downside to this is that you must trust MyBitcoin.