I'm asking this question because I don't want to spend time writing some code that duplicates functionalities of the OpenGL drivers.
Can the OpenGL driver/server hold more data than the video card? Say, I have enough video RAM to hold 10 textures. Can I ask OpenGL to allocate 15 textures without getting an GL_OUT_OF_MEMORY error?
If I can rely on the driver to cleverly send the textures/buffers/objects from the 'normal' RAM to the video RAM when needed then I don't really need to Gen/Delete these objects myself. I become limited by the 'normal' RAM which is often plentiful when compared to the video RAM.
The approach "memory is abundant so I don't need to delete" is bad, and the approach "memory is abundant, so I'll never get out of memory errors" is flawed.
OpenGL memory management is obscure, both for technical reasons (see t.niese's comment above) and for ideological reasons ("you don't need to know, you don't want to know"). Though there exist vendor extensions (such as ATI_meminfo) that let you query some non-authorative numbers (non-authorative insofar as they could change the next millisecond, and they do not take effects like fragmentation into account).
Generally, for the most part, your assumption that you can use more memory than there is GPU memory is correct.
However, you are not usually not able to use all available memory. More likely, there is a limit well below "all available RAM" due to constraints on what memory regions (and how large regions) the driver can allocate, lock, and DMA to/from. And even though you can normally use more memory than will fit on the GPU (even if you used it exclusively), this does not mean careless allocations can't and won't eventually fail.
Usually, but not necessarily, you consume as much system memory as GPU memory, too (without knowing, the driver does that secretly). Since the driver swaps resources in and out as needed, it needs to maintain a copy. Sometimes, it is necessary to keep 2 or 3 copies (e.g. when streaming or for ARB_copy_buffer operations). Sometimes, mapping a buffer object is yet another copy in a specially allocated block, and sometimes you're allowed to write straight into the driver's memory. On the other hand, PCIe 2.0 (and PCIe 3.0 even more so) is fast enough to stream vertices from main memory, so you do not even strictly need GPU memory (other than a small buffer). Some drivers will stream dynamic geometry right away from system memory.
Some GPUs do not even have separate system and GPU memory (Intel Sandy Bridge or AMD Fusion).
Also, you should note that deleting objects does not necessarily delete them (at least not immediately). Usually, with very few exceptions, deleting an OpenGL object is merely a tentative delete which prevents you from further referencing the object. The driver will keep the object valid for as long as it needs to.
On the other hand, you really should delete what you do not need any more, and you should delete early. For example, you should delete a shader immediately after attaching it to the program object. This ensures that you do not leak resources, and it is guaranteed to work. Deleting and re-specifying the in-use vertex or pixel buffer when streaming (by calling glBufferData(... NULL);
is a well-known idiom. This only affects your view of the object, and it allows the driver to continue using the old object in parallel for as long as it needs to.
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