TL;DR answer: GPUs have far more processor cores than CPUs, but because each GPU core runs significantly slower than a CPU core and do not have the features needed for modern operating systems, they are not appropriate for performing most of the processing in everyday computing. They are most suited to compute-intensive operations such as video processing and physics simulations.

GPGPU is still a relatively new concept. GPUs were initially used for rendering graphics only; as technology advanced, the large number of cores in GPUs relative to CPUs was exploited by developing computational capabilities for GPUs so that they can process many parallel streams of data simultaneously, no matter what that data may be. While GPUs can have hundreds or even thousands of stream processors, they each run slower than a CPU core and have fewer features (even if they are Turing complete and can be programmed to run any program a CPU can run). Features missing from GPUs include interrupts and virtual memory, which are required to implement a modern operating system.

In other words, CPUs and GPUs have significantly different architectures that make them better suited to different tasks. A GPU can handle large amounts of data in many streams, performing relatively simple operations on them, but is ill-suited to heavy or complex processing on a single or few streams of data. A CPU is much faster on a per-core basis (in terms of instructions per second) and can perform complex operations on a single or few streams of data more easily, but cannot efficiently handle many streams simultaneously.

As a result, GPUs are not suited to handle tasks that do not significantly benefit from or cannot be parallelized, including many common consumer applications such as word processors. Furthermore, GPUs use a fundamentally different architecture; one would have to program an application specifically for a GPU for it to work, and significantly different techniques are required to program GPUs. These different techniques include new programming languages, modifications to existing languages, and new programming paradigms that are better suited to expressing a computation as a parallel operation to be performed by many stream processors. For more information on the techniques needed to program GPUs, see the Wikipedia articles on stream processing and parallel computing.

Modern GPUs are capable of performing vector operations and floating-point arithmetic, with the latest cards capable of manipulating double-precision floating-point numbers. Frameworks such as CUDA and OpenCL enable programs to be written for GPUs, and the nature of GPUs make them most suited to highly parallelizable operations, such as in scientific computing, where a series of specialized GPU compute cards can be a viable replacement for a small compute cluster as in NVIDIA Tesla Personal Supercomputers. Consumers with modern GPUs who are experienced with Folding@home can use them to contribute with GPU clients, which can perform protein folding simulations at very high speeds and contribute more work to the project (be sure to read the FAQs first, especially those related to GPUs). GPUs can also enable better physics simulation in video games using PhysX, accelerate video encoding and decoding, and perform other compute-intensive tasks. It is these types of tasks that GPUs are most suited to performing.

AMD is pioneering a processor design called the Accelerated Processing Unit (APU) which combines conventional x86 CPU cores with GPUs. This approach enables graphical performance vastly superior to motherboard-integrated graphics solutions (though no match for more expensive discrete GPUs), and allows for a compact, low-cost system with good multimedia performance without the need for a separate GPU. The latest Intel processors also offer on-chip integrated graphics, although competitive integrated GPU performance is currently limited to the few chips with Intel Iris Pro Graphics. As technology continues to advance, we will see an increasing degree of convergence of these once-separate parts. AMD envisions a future where the CPU and GPU are one, capable of seamlessly working together on the same task.

Nonetheless, many tasks performed by PC operating systems and applications are still better suited to CPUs, and much work is needed to accelerate a program using a GPU. Since so much existing software use the x86 architecture, and because GPUs require different programming techniques and are missing several important features needed for operating systems, a general transition from CPU to GPU for everyday computing is very difficult.