http://en.wikipedia.org/wiki/Classful_network

R3 is configured to use classful routing. With classful routing, the router first matches the Class A, B, or C network number in which a destination resides. If the Class A, B, or C network is found, Cisco IOS Software then looks for the specific subnet number. If it isn't found, the packet is discarded, as is the case with the ICMP echoes sent with the ping 168.200.1.1 command. However, with classful routing, if the packet does not match a Class A, B, or C network in the routing table, and a default route exists, the default route is indeed used--which is why R3 can forward the ICMP echoes sent by the successful ping 10.1.1.1 command.

In short, with classful routing, the only time the default route is used is when the router does not know about any subnets of the packet's destination Class A, B, or C network.

So, if the destination address is 168.200.1.1, the classful B network is 168.200.0.0, correct? Since there aren't any subnets of this network in the routing table, shouldn't the ping 168.200.1.1 succeed by using the default route?

It should be using the default route yes, but what about return traffic? What does the route table look like on the responder? What happens when you traceroute? What happens when you ping with a source address of your Ethernet interface?