What happens when a router has two routing protocols running and is receiving similar routes from each routing protocol?

Easy question, right? The routing protocol with the lower administrative distance has its routes installed in the routing table (routing information base - RIB).

However, an interesting question that comes up from time to time is this:

What if I configure the administrative distance to be the same for two routing protocols? Will the router install routes from each routing protocol and allow me to load balance traffic?

The answer is NO. A route for a specific prefix can only be installed in the routing table by one routing protocol. For example, you cannot have a route to the prefix /24 exist in the routing table from both EIGRP and eBGP. So lets say you configured EIGRP to have the same administrative distance as eBGP (20). Which route to /24 will be installed? When there is a tie of configured administrative distance settings the router will use the default administrative distance to make the decision.

equal distance routing protocols

In this case, since eBGP has lower default administrative distance than EIGRP (20 vs. 90), only the route from eBGP will be installed in the routing table (RIB).

Routing protocol admin distance reference: http://www.cisco.com/warp/public/105/admin_distance.html