At least for X86, the answer is that only AMD and VIA have the rights to use the architecture. VIA makes very few CPUs nowadays (I don't even know if they still manufacture the VIA Nano series anymore), leaving AMD is the only other company that designs X86 CPUs. And at least for consumer level products, X86 reigns supreme; there are currently no other CPU architectures out there that can run Windows, so X86 remains dominant by default.
EDIT
I should note, the X86-64 patents are owned by AMD, so Intel and AMD have a rather robust licence agreement between them that allows them to share the rights to both X86 and X86-64 between them. There are a lot of special agreements in place in case AMD either goes bankrupt or is purchased by another company, but essentially, Intel has permanent rights to use X86-64, and AMD looses the X86 license if it ever goes bankrupt or is acquired by another company.
END EDIT
As for other architectures:
ARM: Pretty much everyone has an ARM license at this point. I think even Intel still has theirs from the StrongARM days...
POWER: IBM
Power PC (Legacy): IBM, Texas Instruments, Motorola
68k: Motorola (Yes, there are still plenty of 68k processors used in embedded systems)
Z80: Zilog
For legacy CPUs, companies like Zilog and Citrx used to make pin-compatible X86 chip designs by reverse engineering, but those days are long gone due to the cost of reverse engineering and designing a new chip from scratch.