Personally I'd use "with" with normal nouns, but "of" with gerunds (e.g. "I'm bored of doing..."). I never realised "of" wasn't considered correct until I read Chris and Girdhari's comments.

Both are acceptable. As you can see from the other answers, there are some regional differences.

As per Oxford Dictionary, the standard usage is "bored with," which is used in formal speech and writing. And the more recent and common usage is "bored of." BUT it is NOT used in formal speech and writing. So, both have the same meaning, but one is standard, and the other is common.

"Bored of" is more common. "Bored with" has the same meaning and nuance. You can use either and they are both correct. http://www.oxforddictionaries.com/words/bored-by-of-or-with

I would always say 'bored with'. Bored of does not sound right - although I suspect I have heard people say that.