Updated: Jun 29
Most smartphones, tablets, and computers only allow pairing with one Bluetooth enabled device at a time. Although, I have seen some devices allow multiple connections.
You often won't even realize when devices are connecting to one another via Bluetooth, it's a good idea to occasionally pop open your settings app on your phone (or any other device with Bluetooth connectivity), head to the Bluetooth tab, and take a look at all the devices that could potentially connect and note anything that is, in fact, already connected.
If you ever get rid of a Bluetooth device or plan not to use it for a long time, you should opt to "Forget this device" in your Settings app so you know you are maintaining control of the connection.