I frequently hear this and occasionally see this.

Problem:
“Pronounciation” is a misspelling and mispronunciation that makes the writer or speaker sound dumb.

Explanation:
“Pronounciation” is an ignorant conversion of the verb “pronounce” into a noun.

For fun, I searched Google for each of the following words (with the quotation marks, to avoid variations) and got about the indicated numbers of matches:

• “pronunciation” — 20,700,000 matches
• “pronounciation” — 1,130,000 matches

This tells me that Web authors have written the correct word vs. the incorrect word by a ratio of 18.3-to-1, which is not good, especially given more than a million matches for the incorrect word.

Solution:
“Pronunciation”