This generally depends on the construction of the paragraph.

If the colon is acting in a similar way to a comma and you've yet to complete the sentence, it is preferred that the word directly following the colon starts with a lower-case letter. For example:

There is only one thing left to do now: confess while you still have time.

An independent clause following must begin with a capital letter, as a new sentence would ordinarily. Example:

There were two reasons for a drop in attendance at NBA games this season: First, there was no superstar to take the place of Michael Jordan. Second, fans were disillusioned about the misbehavior of several prominent players.

Think of a colon as a gate, inviting you to carry on into the next part of a clause, or a new sentence altogether.