You can definitely have a lot. My phone is paired with my car, my wife's car, a second connection for audio in my car (the first is just for calls), a jambox, a Bluetooth headset for calls, a stereo Bluetooth headset for music, my pebble watch (which has two connections), a Keyboard, and now with iOS 8, my iPad.
Obviously they're not all active at once, but often multiple devices are active simultaneously. I've never had any issues.