Definition of "processor:" A CPU that has to be attached to a motherboard. May or may not have integrated graphics. Does not contain other computer parts such as memory (other than parts crucial to the functioning of a modern processor such as registers and cache), sensors, connectors (other than the socket), etc.
Definition of "individually:" Is not contained as part of a mandatory bundle. Is not a part of a "system on a chip" or other similar constructs.
Definition of "can be purchased by the average joe:" Does not require a corporate contract. Does not require a phone call to the company. Does not require a bunch of hoops to be jumped through. Can be bought at a quantity of 1.
Companies that are included in "x86:" Intel, AMD, and other minor x86 manufacturers. (Even though other architectures by Intel such as IA32, etc. are completely different from x86, I am not interested in them)
Other preferable things: Motherboards, Memory, and all of the other components required to make a working personal computer (luxuries excluded) to be available.
This question was asked out of curiosity, but it may have practical applications as I am a very casual hobby operating system developer looking to dabble in non-x86 architectures.
I find it hard to believe that x86 is the only computer architecture that you can actually purchase individual components for and build a personal computer. If that is the case, that is really a shame =(
Further clarification: I am looking for a socketed CPU