I'm using a first-gen i3 (@ 4ghz) since release, and recently paired it with a 7950. So far there's no 'casual' games I can't max out, and I get decent frames with lots of eye candy in *many* modern games.
When you read the system reqs, most modern, non-casual games require 2 cores around 2.4ghz, and recommend 4.
Sometimes you might have to turn down CPU intensive options. Things like ragdolls and other physics, AI traffic/people density, etc.
Some games are good at telling you which options are CPU intensive and which are GPU, others it's just trial and error.