MMX are a set of Multi Media Extensions to the x86 instruction set, and pretty much the first "forward step" in the x86 ISA for quite a while.
They are essentially SIMD instructions for Integer Operations, and first introduced with the Pentium MMX processor.
SSE and SSE2 DO NOT replace/supercede MMX, but rather complement it, as they are for Floating Point operations.
All Intel processors since the Pentium MMX (which was introduced in 1997, after the Pentium Pro), and all AMD processors since the K6, include the MMX instruction set.
Intel doesn't make much of a fuss over MMX these days since all processors support it. Their application and performance increase is limited to DSP type functionality, and assist most with video playback and WinModems (Host Signal Processing).