There are a couple of different reasons to have multiple NICs in a server.
A "multi-homed" server is configured to provide network services to more than one subnet so it primarily addresses routing and segmentation rather than bandwidth issues. In my environment, we use this strategy to allow a single server to efficiently serve two VLANs on different subnets.
Another reason to use multiple NICs is to increase bandwidth between the server and the network core. As one example, a Compaqserver and a Cisco switch can be configured to bond four FastEthernet full-duplex connections into a single virtual connection with a potential bandwidth of 800mbps.
A third reason might be to provide routing redundancy so if one path to the server fails, there is another path available. As with the first case, there is not a direct bandwidth advantage but there is a reliability advantage.
And finally, as the first answer suggested, a second NIC can be used to segregate backup traffic from production traffic and that has a definite bandwidth advantage.
So the answer to your question is: "It depends". And what it depends on is the rest of the system design.
paul