That's actually kind of a split question.
As far as the MIPS CPU, anything newer (larger in its series number) than the R4000 is (I'm fairly certain, would have to re-check the MIPS docs) a 64-bit capable CPU. MIPS CPUs are also unusual in that they are capable of running in both 'big-endian' and 'little-endian' modes.
IRIX on MIPS, on the other hand, has a different support structure for the 'bit-ness' and 'endian-ness' of the code it runs. IRIX runs big-endian, 32-bit 'old style' (o32) or 'new style' (n32) code. After IRIX 6.0 (? Could've been 5.0), it was also capable of running straight 64-bit code.
So, to answer your question with an answer, anything after the MIPS R4000 CPU is capable of running 64-bits. What it's actually running depends on the OS/mode.