The usual way to counter the Traxler is 1 e4 e5 2 Nf3 Nc6 3 Bc4 Nf6 4 Ng5 Bc5 5 Bxf7+ Ke7 6 Bb3. Of course, there's much more to it but those moves give white an advantage and dodges black's traps.
The Dreaded Traxler Counter Attack

Thanks! But what if black plays 3.h6? That's what typically happens. I like this though I'll use it if I get the chance.

Don't take the bishop, Move your king to f1 and then get a good defence on it some how. If you get into the Traxler you're basically screwed.

3...h6 is not played often(2 main lines are Nf6 and Bc5). It does prevent Ng5, but it is not a developing move.
Immediate d4 is the strongest move IMO, 0-0 and c3 are also fine(chessgames.com opening explorer):
4. O-O | 21 |
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4. d4 | 15 |
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4. c3 | 7 |
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The Traxler is a defense (or possiby a counter-attack) for Black, not an attack for White. (If Black plays 3...h6, it's not the Traxler (or the Wilkes-Barre as it's cometimes called.) I believe the 5.Nxf7 line is considered theoritically better for White, but I also believe that the 5.Bxf7+ line is more difficult for Black in the practical sense.
It was invented by Fr. Karel Traxler, a Czechoslovakian priest back in 1890. His debut looked like this:
Here is no less a player than Karpov in his heyday playing 5.Bxf7+ and could only muster a draw. Black's repsponses in the first dozen moves or so are pretty much standard.

Thanks so much! Just another reason to open with D4. lol I should practice my d4 openings come to think of it... Though I don't see why gm's will sacrifice so much material to get to the mate.. I mean what if you screw up? You're screwed!

Wow... That game was just amazing! I could never pull something like that off though.. Is that position playing?
This attack is the kind of thing that could keep a chess player up for hours at night. Or at least me. My typical opening as white looks exactly like it but I never actually execute it... This one player the other day used it on me and beat me with it twice. What is a good way to counter it?