space-grade microcontrollers
Space-grade microprocessors started with the RCA 1802 (1976), which used Silicon on Sapphire semiconductor process technology, and gave it a degree of resistance to radiation and electrostatic discharge (ESD). It was used in multiple spacecraft, including the Galileo probe which had multiple 1802 microprocessors on board.  It is still being sold.  The 1802A is the hardened version.  The space shuttle used both an 1802 and 8086 (later upgraded to 80386), plus core memory which was impervious to radiation.

This page gives a run-down of microcontrollers and microprocessors used since then, last updated in 2012.  The latest listing is for the New Horizons spacecraft which just passed Pluto.  It uses a Mongoose-V processor made by Synova, which is a radiation hardened and enhanced version of a MIPS R3000.  These chips costs between $20K and $40K apiece according to the listing cited above.

Surprisingly, there are a number of 80x86 processors, and also a 80C85 used by the Sojourner on Mars.  The Hubble runs on a 80486.  I assume these are all special versions that are radiation hardened, though I wouldn't know where to buy them today.

Other recent radiation-hardened microprocessors are the RAD6000 and the RAD750, both based on the POWER PC architecture.  Both very expensive.

I didn't see any ARM-based microprocessors in the list.