Petrov’s Defense

I've seen 3 Nxe5, 3 d4, 3 Bc4, and 3 Nc3 suggested.

All these options are playable, yes.

I beg to differ with 3.Bc4.  Is it playable?  Maybe.  But it is clearly weaker than the other 3.

The other 3 mentioned are all fine.  I play 3.Nxe5, but nothing wrong with 3.d4 or 3.Nc3.

3. Bc4 is not a good move. 3... Nxe4 and black is ready to play 4. ...d5 unless white plays 4. Nc3 but then Nxc3 and White has lost a lot of the initiative. 

3.Bc4 is a trappy move in fact, but yeap....not excellent

It pretty well forces Black to play f6, though, which weakens his K-side.

It doesn't force Black to play f6 at all idiot. I never play f6 with it. I play Be7. 

"wins the pawn back"

Is that supposed to be some sort of argument that it's not good? You think black should come out with a pawn ahead after three moves?  

Also d6 would be a stupid and losing move but not because the pawn is won back.     

lol, yeah the question is a dark sign. Either start over again or enjoy lifetime 900 rating.

I don't see anything wrong with the question.

LOL, the guy you aggressively and childishly called an idiot is rated almost 500 Elo above you.

Bc4 is fine. White is guaranteed to win the pawn back, and it's great for those not looking for a draw playing the Petrov's.

I like this line as black (I play the Petrovs quite often) 

The line above has won me many many games.

edit: Rather than getting drawn into an argument I will just say next time try looking at the chess, what the actual theory is, what the titled players are saying and what stockfish says rather than people's ratings. It's just annoying to see something like that when it's the main way you play and is perfectly good for black when he wants to avoid the complications of f6 while d6 given as the supposed alternative would be disastrous and the very first thing you ever learn about that opening. It's not a mistake you'd routinely make.  Also Daily doesn't mean anything. 

What's the Petrov? Do you mean Petroff Defence?

Since the man was a Russian, the Russian version of his name (Petrov) is correct.

It's Петро́в.

Petrov was also of course the name of the Soviet lieutenant who ignored equipment stating there were missiles incoming from the USA, bravely hoping it was a malfunction of the equipment which it was. If he had reported it, a nuclear war could have been triggered. A movie was made from the incident called "The Man Who Saved the World". 

Stockfish says that f6 is the best move and that your move passes the advantage back to white.