inIn principle, "packet sniffing" is not a job of routers. routersRouters don't inspect the content of a packet, they just pick the header of the packet and find a suitable exit interface so that it will reach the destination stated in the packet's header.
However, your packets could be sniffed by anyone interested while the packets are moving. interestedInterested bodies ( oftenoften called attackersattackers) can stop your packet and sniff it before it reaches the destination, this. This is called active sniffingactive sniffing, and is performed by firewalls. Another way of sniffing is passive sniffingpassive sniffing. This method involves collecting copies of your packets passively, wireless. Wireless sniffing is a popular attack method in this category.
You can reduce such risks by using encryption techniques discussed above.