More than likely you have like Intel onboard graphics or a very low end nVidia or ATI. The quickest answer to your question is yes. Technically IGP chips can play some games, but only ones that are not graphics intensive. If you want to be able to play your games without them looking blocky like legos or have the men walk like gumby due to low frame rates, then do yourself a favor and spend the $$ to get a decent video card. In fact there is a guy in the FS section selling at GTX 260 for $100 which will in fact play most games without issues.
Just my