This is another softball question and one that CCNAs are often asked. Classful routing protocols are ones that strictly follow the Class A (8-bit prefix), B (16-bit prefix), and C (24-bit prefix) address boundaries.
Examples include RIP and IGRP. Classless routing protocols are ones that throw out the traditional rules of classful routing and allow summarization of routes into smaller, more manageable groups.
Classless routing is also known as supernetting and formally known as Classless Inter-Domain Routing (CIDR). For example, with the traditional Class C address of 192.168.16.0/24, a classful routing protocol would advertise only the /24. Every network device on the network would share the same subnet. If you had subnetted your network to use 192.168.16.16/25, you would have to advertise this more specific route using a classless routing protocol. The same applies to summarization or aggregation. If you have multiple Class C networks such as 192.168.16.0/24 and 192.168.17.0/24, using a classless routing protocol, these routes could be written as 192.168.16.0/23. Classless routing protocols include EIGRP, OSPF, RIPv2, and BGP.