Robotization refers to the imprisoning of Sonic's animal friends inside badniks - a technique which seems to be Dr. Robotnik's favourite hobby during the early Sonic games. It is distinct from the considerably more intensive technique of roboticization, where robots are created by actually transmuting flesh into metal - a process portrayed principally in the SatAM and Archie continuities, but which also appears in Sonic Chronicles: The Dark Brotherhood.
From Sonic the Hedgehog (16-bit) to Sonic & Knuckles for the Sega Genesis, Doctor Robotnik's mechanical legions ("badniks") used small animals as a kind of "organic battery". Robotization referred to the imprisonment of a creature inside one of these robots; the organic creature remains intact and viable, but trapped and presumably not very happy. When defeated by Sonic, Tails, or Knuckles, the badnik would explode and the trapped creature be set free.
Although Robotnik has branched out from the use of living creatures as power sources in later model robots, the classic animal-containing badnik still appears in some of the more modern games, including Sonic Advance 1 and 2.
Sonic Spinball sees the blue hedgehog attack Robotnik's facility on Mount Mobius. At the core of the Doctor's facility lies the Veg-O-Machine, a mass-robotizer device which can transform woodland critters into robots in mere seconds. This is the only instance within the games where the process of robotization has been directly observed.
What may or may not be another robotizer appears in Sonic CD. In his operations on the Miracle Planet, Robotnik used plant seeds instead of animals as a power source for his badniks. Travelling into the past allows Sonic to find a crackling robot teleporter, which, if destroyed, obliterates all badniks across all time frames within the Act in question, paving the way to acheiving a Good Future. The device is inactive if found in the present or Bad Future, while the robots keep rolling.