Note: There is one more robot in this game called Liberty Prime, but because he's one of a kind he'll get his own screenshot. The Mister Handy, the Miss Nanny, the Mister Gutsy, the Eyebot, the Protectron, the Robobrain, the Sentry Bot, and the Assaultron.
Here a group of screenshots of the types of Robots in Fallout 4.