There are no modern PC's sold without GPU. Every computer available to the average consumer needs a graphics unit in order to function (even if just in VGA mode). What you are seeing is PC's sold without a discrete graphics card, in which case the GPU is just a little chipset soldered on the motherboard, or, more recently, directly integrated into the CPU itself (so that buying the processor gets you the graphics card as well, if your motherboard supports it and if you aren't looking to use a discrete one instead).
Games and applications will work exactly the same as the drivers for those GPU's still implement DirectX/OpenGL/etc.. though perhaps not every feature, and certainly not at the same speed as a full-fledged graphics card, but, in short, you don't need any special code to write applications for them, the HAL (hardware abstraction layer) takes care of everything - barring driver bugs, anyway.
Many people use this option when they find integrated graphics cards sufficient for their needs. They won't be playing the latest Crysis on it, but for a lot of people (for instance, which only browse the internet and play light games, or even office desktops) that doesn't matter at all, so they use it because it's cheaper and uses less power.
For instance the CPU I am using right now (sandy bridge i5) has an integrated graphics card, but I have never used it, as I already have a discrete graphics card and in any case my motherboard does not support integrated graphics cards (you'll find it's often either/or, few desktop motherboards let you switch between both, with laptops though they are usually designed to be able to switch at will in order to save battery life).
EDIT: just to clarify, even if you are running a headless server you do need a graphics card. Your computer will *not* boot without one (so if you are running headless, an integrated graphics card is actually ideal as it takes no space and gets the job - no job - done, unless for some reason you want to do GPU computation on your server). For actually using a screen, the above applies as well.