How should I play against the Philidor defense? As white, I often encounter the Philidor Defense by black:  

[FEN ""]

1. e4 e5
2. Nf3 d6


I usually play Nc3 or d4 on the next move, but is this the best move? What are some lines (advantages or disadvantages) against the Philidor?
3. d4 is the usual move after 1. e4 e5 2. Nf3 d6.  Chess Opening Theory states that it is probably the best move, and also concedes 3. Bc4:

The best move is probably 3. d4. White threatens a queen exchange with dxe5 dxe5 Qxd8+ Kxd8 and Black can forget about castling. It puts pressure on the center and the Black fortress may collapse at any time.
Another possibility is 3. Bc4 leading to a more positional game, playable for both camps.

Fred Reinfeld suggests the following line (exclamation marks are his) as in this game.  White maintains a sharp edge:
[FEN &quot;&quot;]
1. e4 e5 2. Nf3 d6 3.d4 exd4 4. Qxd4! Nc6 5. Bb5! Bd7 6. Bxc6 Bxc6 7. Nc3 Nf6 8. Bg5 Be7 9. O-O-O

A good resource to study would be shredderchess.com's opening database.