The Difference Between Fast Path and Slow Path
To better understand the text below, it's highly recommended that you download this short 4 minute animation to better understand the text below.
A router typically has what is called a fast path and slow path. The fast path is optimized for doing one job and doing it really well - the expeditious handling of routing IP packets. (See diagram). 
Traceroute and Ping actually work in slight different ways. Here's a detailed explanation of Ping and here is a detailed explanation of Traceroute. The important issue is that to process both Ping and Traceroute requests, the destination router must send the packets down to the slow (admin) plane in order to process. This administration plan (my term) is simultaneously tasked with handling internal router functions such as network management, command line interface, monitoring and other tasks. How well the admin plane responds to ICMP requests typically has little correlation with how well the router is doing its primary job: routing packets! Fortunately the routers precede the destination router will process the packets normally.
To see what this looks like in terms of a network diagram, refer to the diagram above. In the top picture, note that when a trace or ping to the end destination is performed, all the packets are traversing the fast plane of the intervening routers. In the bottom picture, the same applies to the first two routers but in this case since the third router is the destination, the router must send the packets down to the slow plane for processing. Once complete, the results are sent back up to the fast plane and returned to the source to answer the query.