What the highest possible IQ?

Actual IQ test scores average 100 for the global population. There are various scales, including the Weschler and the Stanford-Binet.

William James Sidis's IQ was estimated to be anywhere from 250 to 300, but this was before either scale mentioned above had been established. Further, Sidis never took an IQ test. He also left posterity very little. He could speak over 40 languages.

Albert Einstein is said to have taken a Weschler test in the 1940s, and scored 186. Many famously intelligent people never took an IQ test, since none had yet been devised during their lifetimes, and thus these peoples' IQs are utter estimates and most likely very inaccurate. Nevertheless:

Wolfgang Amadeus Mozart - 160

Sir Isaac Newton - 200

Garry Kasparov (chess player) - 190

Leonardo da vinci - 220

Bobby Fischer (chess player) - Tested at 187

The highest actual score ever recorded is supposedly 228, by Marilyn Vos Savant, but there is no confirmation to be found on the Internet, and regardless, she has done very little with her abilities.

In general, no test scales accurately beyond about 180. Genius level is usually defined as about 140+.