Bitcoin-Qt is the original Bitcoin client.
Leaving it open has no real consequences considering yourself individually, but there are some minor effects.
Effects regarding you:
When you leave your client open, your client will always be in sync with the network, meaning that you can always see your accurate balance. If you should close it, it will have to catch up syncing before it can show you your addresses' balances.
As explained in this answer, when you send a transaction into the network, there is a small chance that it may get lost. In that case, when your client is still open, it will re-transmit the transaction automatically. When your client is closed, the transaction will be lost and never confirmed. Note that the chance that a transaction gets lost is very small.
Effects regarding the Bitcoin network as a whole:
Bitcoin is a peer-to-peer system, in which all Bitcoin clients function as nodes. But not every node knows of the existence of all other nodes. A transaction is made by sending it to all nodes in the network. When your client is open and connected to the network, it has a list of other nodes it knows about. When one of them sends a transaction to all the nodes it knows, you help him by sending it forth to all the node you know about. This way you can help reduce the time it takes for a transaction to reach the whole network.
Together with relaying transactions, your client will also check all transactions it receives. It is possible that some of them is malicious, meaning that the sender does not have the right to spend the bitcoins he is spending, or that these bitcoins are already spent. In that case, your client will ignore the transaction and not relay it.
Another thing your client does is helping new nodes synchronize. When a new client enters the network, it has to build the block chain from scratch. It will request other nodes to send parts of it to him so that he can save them. When your client is open, it will help other users download the block chain.
Note that it is not an effect of leaving your client open that your bitcoins are less protected. Encrypted wallets are only decrypted for spending bitcoins.
Also, your client will not mine while it is open, so the process it not very resource-consuming.