I run PES 2012 and minecraft lowered with my 256MB GPU without a problem. Also, graphics doesn't depend on memory, because almost all the time graphics depend on the GPU.
What is it anyway? Intel HD 3000? HD 2000? Or AMD HD 6410D? HD 6550D?
Well you have a semi decent setup besides your IGP. Half Life Source games work decently on IGPs.
Other than that....you might be able to play some other newer games on low quality. But if your serious about gaming you will definately need a GPU. Something along the lines of a 6770 which is a good mid range GPU, and decently priced.