Is this pawn endgame drawn or won?

I think it's a draw.

I checked an endgame tablebase; with white to move it's a draw with perfect play on both sides (no mistakes).

This is a draw. Provided Black plays correctly.

When white moves e4, as he must to save the pawn, then Black must go straight back e7 in order to take the opposition on whatever side white moves to. 

This is a draw with either side to move (provided black makes the best and simple moves.)

Checking a tablebase can be instructive as mentioned above, but reviewing it in an endgame book, perhaps with a friend or vs. Fritz may be more illuminating for some.

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is adraw1!!

Here is the position with perfect play from both sides.

Its a draw

the critical squares for white with a pawn on the 5th rank are the 3 squares on the sixth rank in front of the pawn.  if white can get his king to one of those squares ( in this case (d6, e6, f6) then white wins, else it's a draw.

Black can keep white's king from reaching those critical squares by playing Ke7 after white plays Ke4 (as was mentioned earlier).  After that if white pushes the pawn black takes, and if white moves his king adjacent the pawn, (like Kf5), black moves his king to directly oppose white's (with black ...Kf7), which prevents white's kind from reaching a critical square.  If white pushes, the situation just repeats until black is stalemated on the 8th rank.  (1. Ke4 Ke7 2. Kf5 Kf7 3. e6+ Ke7 4. Ke5 Ke8 5. Kd6 Kd8 6. e7+ Ke8 7. Ke6   stalemate).

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 LOL. If that is the best you can do in an attempt at humour, your future doesn't look to bright

draw, its basic opposition theory

The logic to understanding this ending is simple: Black keeps his king in front of the pawn whenever he can (to keep it from moving forward), and in front of the White king when he can't (to keep the White king from getting in front of the pawn). If the White king can get in front of the pawn White wins. For example: 1.Ke4, Ke7 2.Kd5, Ke8?? 3.Ke6, Kd8 4.Kf7, and the pawn queens.