Which IP Routing Protocol Is Used Best For Which Circumstances? RIP EIGRP OSPF BGP

EIGRP is best because this is hybrid protocol .Eigrp support both link state and distance vector .

for internally routing ISIS and OSPF is the best then EIGRP

for external routing BGP is the best

RIP, EIGRP and OSPF are Interior Gateway Protocol and are used to communicate in a single Autonomous System (A.S). 

BGP is an Exterior Gateway Protocol and is used to communicate between different AS.

Autonomous Syste (AS) is basically a single network or multiple network managed by a signle Network Admin.

RIP is not used these days because of multiple reason as it sends the full routing update periodically thus higher utilization occurs on the router and also it's max hop count is 15.

EIGRP is a distance vector routing protocol but is not widely used as it was a CISCO Propreitary Protocol. Only CISCO router's can be configures and communicate uing EIGRP.

OSPF is a links state protocol and is an open standard, thus it is most widely used. Moreover, OSPF has area concept which decreaes the router utilization.