I would say that, if you have a cheap motherboard, then you will hear a difference.
A sound card as cheap as the Xonar DG may be a good starting point, but the possibilities are almost seamless among Auzentech, Creative and Asus. Generally people recommend the Xonar series for good audio quality in cheap format. You should also take into consideration if DSP effects is something you'll be interested in. For gaming, people seem to prefer CMSS-3D which is available in the Creative X-Fi series as well as some of the Auzentech cards. The Xonar series all uses Dolby Headphone. The best consumer oriented sound cards on the market today in respect to sound quality and customizability are the Xonar Essence ST/X and the X-Fi Titanium HD.
In my case, I have pretty competent onboard sound called ACL888 which has quite good DAC, however, since it's Realtek it does not come with any DSP, at least nothing that matches that of the Creative and Asus cards - so I went straight for the Essence card. However, DSP is something to consider only for movies and games. If music is your primary activity then I would recommend the Xonars.