PC 1 in subnet - 192.168.1.x
PC 2 in subnet - 192.168.2.x
Is it possible to access one pc from the other by its IP address without special router config?
Two different subnets are two separate broadcast domains. The only device that can traverse multiple broadcast domains is a L3-aware device (router, firewall, multilayer switch etc.).
You need a router. If you need a quick and dirty solution that is NOT AT ALL viable in the long term and for networks bigger than 2-3 pc, if they're really in the same L2 network (eg: two pcs connected on the same switch, with no VLANs configured), most modern Operating Systems allow you to configure multiple IPs for any given network card. That way you can give to Computer1 an address in Computer2's subnet and the two pcs are not really in two different subnets anymore :)
You. need. a. router.