A toady, or yes-man, does not get his name because he crawls around like a toad, or because he is despicable like a toad. Toady is short for toad-eater, and it was a job.
Once upon the seventeenth century the world was filled with mountebanks and quacks who would tour around trying to sell their snake-oil cure-alls. To sell, they needed to prove their potion's efficacy, and for that they needed a toad-eater.
Toads, as everybody knew, were poisonous. So the toad-eater's job was to eat one and collapse into a shivering, floccillating heap. The doctor would then give the toad-eater a dose of his patent medicine and, before the eyes of the crowd, the toad-eater would regain his health.
Obviously being a toad-eater was not a great job. Whether or not you actually ate your toad or only pretended to, it was a pretty humiliating way of making a living.
A toad-eater called William Utting is recorded in 1629, and the word was shortened to toady in 1828, by Disraeli.
P.S. I know this all sounds unlikely, but the OED says it's true.