Each core is a pipeline, however the CPU can have multiple cores, each core would have its own L1 cache for data and instructions, L2 may be shared between a couple of cores, L3 is often shared between all of the cores on the die. There is also a memory controller on modern ones, and on LGA 1156 CPUs there is also a PCI-E controller built into the die.
There is far more to a CPU than its pipeline, without the cache CPUs would be incredibly slow as it doesnt matter how quickly you can exectute instructions if the data takes a while to get to you, GPU's often have this problem with memory intensive tasks like AA.
Also realize that a pipeline is not a straight pipe like it seems it should be, there are many branches off of it depending on what type of instruction needs to execute.