Does Uncle Ben know Peter Parker is Spider-Man? If not, why would he suggest Peter has any "GREAT power?"

First off, since you mentioned the comics: in the original comic string, this is not a line spoken by Uncle Ben. Rather, it's an unspoken caption on one of the panels (that is, it's not actually spoken by any character.) However, in later comics, Peter's flashbacks to the days when Ben is alive have shown him saying it, which is where the movies drew their dialogue from.

Within the movie: No, Ben likely has no idea what Peter has become at the time he dies (spoiler alert?). However, in both of the movies thus far, Ben is shown to frequently give Peter advice of a somewhat "preachy" nature. In other words, Ben often quotes sayings of that nature to Peter, even when they don't appear to apply directly to Peter's life. He's a person who has a lot of "folk wisdom" built up, and uses it to try and direct Peter to improve his life.

When Ben says this to Peter, he has just gotten into a fight (due to his Spider-Man powers, but Ben doesn't know that). The dialogue that follows:

PETER I'm trying, Uncle Ben, I am. I feel all this, this (choosing words carefully) power, but I don't know what it means, how to control it, even, or what I'm supposed to do with it.

UNCLE BEN You'll figure it out. You're one smart cookie, Pete, your teachers tell me they've never seen a science whiz like you at this age. Knowledge is power. But with great power comes great responsibility. Remember that.

Ben's choice of phrase is driven by two things here: Peter is the first one to use the word "power", which Ben later turns around with the cliche "Knowledge is power". He's basically admonishing Peter that, whatever "power" Peter thinks he has, he should be responsible with it -- not go around getting into fights over it.

In the 2012 reboot, the scene is a lot more contentious. Peter and Ben are fighting over Peter's failure to pick up Aunt May and walk her home. He doesn't actually say the line exactly as normally quoted, but he does talk about Peter's father having "a philosophy" that is you had the ability to help people, you had a "responsibility" to do it. Again, though, he's speaking to Peter in generalities, in this case, Peter's decision to leave his Aunt in potential danger of being mugged when he had the "power" to help her.

The phrase itself predates Spider-man:

The phrase "with great power goes great responsibility" was spoken by J. Hector Fezandie in an 1894 graduation address at The Stevens Institute of Technology - "The Moral Influence of a Scientific Education", The Stevens Indicator, Volume 11, Page 217.
The exact phrase was repeated during a speech by President Harry S. Truman in November 1950 - Public Papers of the Presidents of the United States: Harry S. Truman, 1950 (published 1965), Page 703.
A UK Member of Parliament implied in 1817 that a variant of it was already a cliché (Thomas C. Hansard, ed (1817). Parliamentary Debates. p. 1227. Retrieved on October 10, 2013. "He should, however, beg leave to remind the conductors of the press of their duty to apply to themselves a maxim which they never neglected to urge on the consideration of government—" that the possession of great power necessarily implies great responsibility.""
The editor is quoting William Lamb (pp. 1125–1229)). The sentiment is also found in Luke 12:48: "from the one who has been entrusted with much, much more will be asked" (NIV).

Those are not spoken in terms of super powers, just strength, and morality.

In fact, the first use of it in Spider-Man is in Amazing Fantasy #15, Spider-Man's first appearance. Uncle Ben doesn't say it. It's just a Aesop's Fable type of moral lesson:

As for the movie, and any modern spidey comic or cartoon, Uncle Ben says it, but has never known Pete is Spider-Man. He always says it as a "You're a Man now, not a boy." lesson of responsibility. Parker has always been top of his class, gifted in brains. When he first gains the powers, he becomes strong, and often the typical teenage attitude. Ben gives him the "Talk" to get him to shape up, but it doesn't work. In Amazing Spider-Man Ben says "If you can do good things for others, you have a moral obligation to do those things. Not choice, obligation".

The Toby Spider-Man film uses the traditional phrase.

But they both have the same thing in common. Parker has been getting into fights, he's staying out, being "suspicious". It's just the phrase a father-figure normally states. Specifically, it's something that Parker also tells a bunch of random people multiple times through cartoon and comic history. He says it to both normal and super powered people. And then they do the same. Spider-Gwen and Kitty Pride

Bonus: In a deleted scene of Amazing Spider-Man 2, Parker's father is alive, and says the same thing. He does not know Parker is Spider-Man.