Should the first word after a colon be capitalized?
"For example: This."
"For example: this."
This can go either way. If you are starting a complete sentence that represents a summation of what came before, you are certainly entitled to capitalize the sentence.
But if you are using the colon to offset a list or other material that does not form a complete sentence, it makes no sense to capitalize what follows:
The answer is culturally dependent. In English, we would not capitalise after a colon (unless the next word was a proper noun). However, it appears that in American English the rules are different... and different depending on whose style rules you are following.
For example, you may follow a colon with a capital if it follows with: