i was wondering if there's any application or way of executing a non gaming application on a gpu on any regular PC, since gpu's are highly parallel they can greatly reduce the workload off a cpu.
i did some research but all i found was some theoretical studies and not actual software capable of doing this.

for more information:

http://www.nvidia.com/object/nvidia_research_pub_008.html
it kinda did, but these are specific applications in which gpu's are used and usually the gpu's are programmable, for example nvidia's TESLA, moreover some applications do exist that benefit from gpus computing power but they are specifically programmed like PS3's folding@home, also all of the internet browsers are becoming gpu based, but what i really wanted to know is that can i program or download a software that will allow me to control my ati's 4870hd gpu and use it in on application of my choice.
No this is not possible.

Although they have similar purposes (computation), GPUs and CPUs are accessed differently. Hardware components of your system are accessed through your operating system. In other words, it is up to the developer to decide where his computation will be executed.

If you look at Samer99's links, you will see that what you suggest makes sense, and developers are indeed trying to take advantage of the GPU for non-graphical computation. But as far as the user (ie yourself) is concerned, you have very little control over your system and cannot determine where it goes (except for specific applications that do give you the choice).
its a shame, ive seen firsthand the processing power of gpu's, specifically the new fermi architecture of nvidia, if only applications and operating systems can be more flexible regrading this matter, we could get the maximum out of our machines.