How many devices we can pair via Bluetooth to iPhone?

(I know this is an old question, but) Apple say

The official Bluetooth specifications say seven is the maximum number of Bluetooth devices that can be connected to your Mac at once. However, three to four devices is a practical limit, depending on the types of devices used. Some devices require more Bluetooth data, so they're more demanding than other devices. Data-intensive devices might reduce the total number of devices that can be active at the same time.

https://support.apple.com/en-us/HT201171

(And, I know this is for a Mac and not an iPhone. But, perhaps this also holds here).

As it stands in iOS 6.1.4, the current limit for Bluetooth Low Energy devices is 10 simultaneous CONNECTIONS (at least on the NRF8002 chipset). Although the BLE spec says it can in theory have an infinite number of connections, the connection will time out when you try to add an 11th device.

As for the pairing table, I've previously had two additional a2dp devices in my pairing table(not connected) and 10 current BLE connections as the maximum. So that is a total of 12 devices in the pairing table on an iPhone 5 running iOS 6.1.4. You could probably have more devices listed in the pairing table, but the one definite is 10 connections is the current max.