IOS can generate numerous SNMP traps, but you have to enable most of them manually. Configuring a server that receives SNMP traps with the snmp-server host address community traps is not enough; you have to enable individual trap categories with the snmp-server enable traps group [ trap ] command.
In older releases, the standard SNMP traps (for example, link up/down traps) are enabled by default and cannot be disabled with the snmp-server enable traps command. Newer IOS releases have added the snmp-server enable traps snmp [ authentication | coldstart | linkdown | linkup | warmstart ] global configuration command. These releases require you to enable standard SNMP traps manually; otherwise the router will not generate them.
If you want to see the whole list, configure snmp-server enable traps and execute show running | include snmp-server enable. IOS 12.4T network management reference guide also includes a comprehensive list of all options.