I'm sick as a dog.

That seems like a stupid phrase to me. I don't know many dogs who really get sick that much. And the ones I have seen sick just sort of slow down. They don't really seem all that bad off.

The World Wide Words website says this:

There are several expressions of the form sick as a ..., that date from the eighteenth and nineteenth centuries. Sick as a dog is actually the oldest of them, recorded from 1705; it is probably no more than an attempt to give force to a strongly worded statement of physical unhappiness. It was attached to a dog, I would guess, because dogs often seem to have been linked to things considered unpleasant or undesirable; down the years they have had an incredibly bad press, linguistically speaking (think of dog tired, dog in the manger, dog’s breakfast, go to the dogs, dog Latin — big dictionaries have long entries about all the ways that dog has been used in a negative sense).