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Stalemate is not the only way a draw can be achieved in the game. The
triple repetition rule ends the game in a draw (1/2 - 1/2), but not a
stalemate. In other words, stalemate is only one type of draw possible.

The triple repetition is not achieved when one player moves a piece in the
same square three times, for then a losing player could force the game
into a draw rather easily. Triple repetition is achieved when the same
board position (meaning all of the same piece types of the same color are
on the same squares) is reached for the third time in a single game.
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To checkmate, a player must have one or more of the following:

1) K & Q,
2) K & R,
3) K & B & B,
4) K & B & N,
5) K & P.

K & N & N can not force a mate. Also if in K & P vs. K, if the pawn is on
either of the rook files (a- or h- files) and the side with just the king
is able get the king on that file (in front of the pawn, impeding the
advance of the pawn), the game is drawn, by definition, as if continued,
the only possible outcome is stalemate.

There are also a few situations, in tournament play, when a draw can be
claimed by a player to a neutral arbitrator (i.e.: tournament steward),
when a player has 'insufficient losing chances'. Examples of such are,
but not limited to:

1) K & R vs. K & R,
2) K & Q vs. K & R,
3) K & B & B vs. K & B,

provided that a piece can not be immediately captured to set up one of the
five situations above.
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If a player is put in a position where only the king can move, it is a
draw after 50 moves (50 for white and 50 for black, totalling 100) without
it being placed in checkmate. However, when counting the 50 moves, the
count must restart when a pawn is moved or a piece or pawn is captured.
So, if a player is unable to mate the king after 49 moves, the player may
choose to simply push a pawn, to get another 50 tries. See 'The 50 moves
rule' for more on this.

Simply remark that
K & Q vs. K & R is winning for the Queen (except if K&R have perpetual
check, or can capture the queen in the very first move)

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what would this be? stalemate or legal?

Pawn White: A1
Pawn Black: A2 & B4
King White: G2
King Black: F7
Rook Black: H6
Bishop Black: H4 & F5

White's turn

I think that it is still a legal game because the king has 5 legal moves
and a stalemate requires no legal moves. I would just like to make sure
with a second opinion.

can a queen jump over another peice to kill a another piece to protect the
king

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I'm playing my electronic chess game at the highest level and it has put
me in 'check',then I move out of 'check', then it puts me back in
'check'. And we are going back and forth, in'check and out of 'check'
and I'm moving my king in the same two squares. 
Is this considered a 'stalemate'? because I think my electronic chess
game wants me to move in a certain square so it can get me in
'checkmate', and I see what its trying to do.
Whats the ruling on this?

The sort of situation you describe generally results in a draw by one of two rules:

The first is the threefold repetition rule, which applies when the exact same game position is repeated three times.  For example, if you and your opponent are each moving back and forth between the same two spaces, once you have come back to your starting position after two full loops, the game can be declared a draw.

The second is the 50-move rule, which applies when there have been no captures or pawn advances (irreversible moves) for at least 50 consecutive moves of white and black.  This is invoked mostly in endgames where the board is very open and so it can take a very long time for (and be difficult to notice when) an exact position is repeated three times.

Of course, the game can end in a draw immediately if both players agree, which may cut these conditions short if it is obvious (for example) that the game is going to end in a perpetual check.

What if the kings are the only pieces on the board

@hcl4: Then it is a draw. The technical answer is from a related page, the 50 move rule: neither player can do much of anything and so 50 moves will pass without a capture or pawn move, and that rule will kick in to say the game is a draw. Of course, since this is bound to happen, both players should just agree now that the game is a draw.

Edit: Actually, looking around a bit more, it appears that (perhaps because of time controlled games) my technical explanation was incorrect. It is a draw because checkmate cannot possibly happen.

To Bill Nye. It is illegal to leave your king in check. When an illegal move is noticed, the rules require all subsequent moves to be retracted and re-done.

I believe there is a mistake in the illustration of the stalemate. The horse should be in G5, not in F6.