According to the main line, Be3 is the best move, follows Bg4, Qd3, with the intention of Qf1. white can follow by developing the knight to d2, etc
Best line against Marshall Attack?
Many lines have been analyzed well over 30 moves out whose final verdict is a draw. Honestly, if I were you, I'd play h3 instead of c3 just to get out of main line Marshall.

Well, I only liked Ruy Lopez because of the Marshall Attack. Then I should take your advices and play Scotch.
Well, I'm not an expert about 1.e4 e5 openings but here's what I think:
Start with the Italian game (modern variation). It's typical piece placement and arising pawn structures are similar to the Ruy Lopez.
Resources: Start with Kindermann's excellent DVD. After watching this you're good to go. http://www.newinchess.com/The_Italian_Game-p-2468.html
If you need more analytical information check out Emms' book. http://www.newinchess.com/Beating_1_e4_e5-p-5026.html
After getting some experience with this opening start experimenting with the Ruy. But before doing so it could be helpful to read a book with verbal explanations about it. I'm recommending McDonald's latest effort http://www.newinchess.com/The_Ruy_Lopez__Move_by_Move-p-7015.html
And a small reminder at the end. You should aim to get positions that you've a clear idea about how you should continue. An equal position that you know your typical plan(s) is preferable to an advantageous position that you don't know anything about. If I were you I'll avoid Marshall (for both sides) like plague until I become a master.

I think melvinbluestone's 15.Bxd5 is a safe way of meeting the Marshall. I would probably choose the same line.
15. Re4 is an interesting alternative.
Obviously an old thread but I hate some of these responses.It was a good valid question and people dont answer it.
"it has been analyzed to a draw 30 some moves deep"
provide those moves thank you.
I hate it when the verdict is just play something else. you may as well not answer at all


5...Qd4 wins it back..

I have done my own extensive analysis of the marshall gambit (from the white side) some years ago, and couldn't find an advantage for white. Therefore, I play anti-marshall today, because I don't like the attack black has going on. It's like walking in a minefield - Only you are most likely to fail, and if you passes the minefield with precise play, the game is only equal.
However, lately Caruana beat Aronian in the Marshall attack in the zürich chess challenge 2014 http://en.chessbase.com/post/zurich-05-caruana-strikes and I think that his way of handling the Marshall could be the way to go, even though I didn't analyze all the possible side variations black could play.
I might be a bit late to this but after 14...Qh3, I like the more aggressive move Re4. A great line to look into if you are keen, however if opponent plays accurately, can force you to end up playing a more strategic and defensive game with some tactics here and there. after 15. Re4 is main line g5, followed by Qf1 to trade queens.
What do you play against it? I am not talking about an Anti-Marshall opening, I am talking about what to do after we enter the Marshall Attack.