user14257: Many beginners open the game with moving their a or h pawns. 
Is there any benefit at all with this opening? 

user14202: There are benefits and drawbacks to each move in chess.  The benefits to h4 or a4 is that they grab space, control squares in the enemy territory, and increase the scope of the rook.
Some of the drawbacks to opening like this are:
1. They don't fight for the center
2. They impact castling options
3. They don't promote the development of the Bishops

user-1: 1. h3 has the potential to transpose into normal openings, as it is quite common to play h3 to prevent ...Bg4 pinning a knight on f3.
For example this move order quickly becomes a four knights Italian game:
[FEN ""]

1. h3 e5 2. e4 Nf6 3. Nc3 Bc5 4. Nf3 Nc6 5. Bc4

One other transposition possibility is that white can play the Grob, but that opening has a dubious reputation.
[FEN ""]

1. h3 e5 2. g4


user1485: GM Hector once opened with 1. h4 and (with a bit of luck) won the game:
[FEN ""]
[Event "Dinard open"]
[Date "1986.??.??"]
[Result "1-0"]
[White "Jonny Hector"]
[Black "Paul Boersma"]

1. h4 Nf6 2. d4 d5 3. Nf3 c5 4. Bg5 cxd4 5. Bxf6 gxf6 6. Qxd4
Nc6 7. Qa4 Rg8 8. c3 Qb6 9. Qc2 Bf5 10. Qxf5 Qxb2 11. e3 e6
12. Qxh7 Rg4 13. Qd3 Qxa1 14. Qc2 Rc8 15. Nfd2 Nb4 16. Qd1 f5
17. cxb4 Qb2 18. Bb5+ Kd8 19. Ke2 Qxb4 20. Bd3 Rxg2 21. Nf3
Bd6 22. Nbd2 Ke7 23. Qa1 Bg3 24. Rf1 f4 25. e4 Rc3 26. exd5
Qc5 27. d6+ Kd7 28. Qb2 Qe3+ 29. Kd1 Qxd3 30. Ne5+ Kxd6
31. Nxd3 Rxd3 32. Qb4+ 1-0

I thought one idea behind the move 1. h4 was to play the Albin Countergambit with the extra attacking move h4,
[FEN ""]
[Title "Reversed Albin"]
[Startply "12"]

1. h4 d5 2. d4 c5 3. e4 dxe4 4. d5

but according to my database this has actually never happened in a real game, so I might be mistaken.
The book Groteske Schacheröffnungen: Wagnis mit Methode (1991, in German) by Stefan Bücher has a chapter about 1. h4. 

user13055: Apart from the fact that you can develop your rooks (which isn't good so early in the opening, because your rooks might become vulnerable), the only other "benefit" I can think of is that a4 (more likely than h4) can be useful after some transposition to a normal opening, e.g. stopping black from playing b5.
That being said, black can comfortably choose (thanks to your gift of a tempo) an opening where a4 is useless.
The other move 1. h4 is even more problematic because castling kingside is much more frequent than castling queenside and h4 weakens the pawn shield in front of your king.

So I don't think it's worth calling these possibilities benefits at all.

user13012: 1.a3 is a semi-respectable opening called Anderssen's Opening, and since he beat Paul Morphy(http://www.chessgames.com/perl/chessgame?gid=1019048) with it, it cant be so ridiculous. He used it to enter an English opening or a reversed Sicilian. I think Larsen once did the same.
There is at least one trap. Black plays a reversed Scotch 1.a3 e5,2.e4 Nf6, 3.Nc3 d5, 4eXd Nxd4 5. Qh5. This move is playable, and very lively, on the fourth move of the regular Scotch, but it's not played much because of 5. Ndb5 which is not available here.
Beginners would probably disapprove of 1.a3, on the grounds that it does not give them enough freedom of action to put their Rook en prise.

14257: <p>Many beginners open the game with moving their a or h pawns. 
Is there any benefit at all with this opening? </p>
 14202: <p>There are benefits and drawbacks to each move in chess.  The benefits to h4 or a4 is that they grab space, control squares in the enemy territory, and increase the scope of the rook.
Some of the drawbacks to opening like this are:
1. They don't fight for the center
2. They impact castling options
3. They don't promote the development of the Bishops</p>
 -1: <p><code>1. h3</code> has the potential to transpose into normal openings, as it is quite common to play <code>h3</code> to prevent <code>...Bg4</code> pinning a knight on <code>f3</code>.</p>

<p>For example this move order quickly becomes a four knights Italian game:</p>

<pre><code>[FEN ""]

1. h3 e5 2. e4 Nf6 3. Nc3 Bc5 4. Nf3 Nc6 5. Bc4
</code></pre>

<p>One other transposition possibility is that white can play the Grob, but that opening has a dubious reputation.</p>

<pre><code>[FEN ""]

1. h3 e5 2. g4
</code></pre>
 1485: <p>GM Hector once opened with <code>1. h4</code> and (with a bit of luck) won the game:</p>

<pre><code>[FEN ""]
[Event "Dinard open"]
[Date "1986.??.??"]
[Result "1-0"]
[White "Jonny Hector"]
[Black "Paul Boersma"]

1. h4 Nf6 2. d4 d5 3. Nf3 c5 4. Bg5 cxd4 5. Bxf6 gxf6 6. Qxd4
Nc6 7. Qa4 Rg8 8. c3 Qb6 9. Qc2 Bf5 10. Qxf5 Qxb2 11. e3 e6
12. Qxh7 Rg4 13. Qd3 Qxa1 14. Qc2 Rc8 15. Nfd2 Nb4 16. Qd1 f5
17. cxb4 Qb2 18. Bb5+ Kd8 19. Ke2 Qxb4 20. Bd3 Rxg2 21. Nf3
Bd6 22. Nbd2 Ke7 23. Qa1 Bg3 24. Rf1 f4 25. e4 Rc3 26. exd5
Qc5 27. d6+ Kd7 28. Qb2 Qe3+ 29. Kd1 Qxd3 30. Ne5+ Kxd6
31. Nxd3 Rxd3 32. Qb4+ 1-0
</code></pre>

<p>I thought one idea behind the move <code>1. h4</code> was to play the Albin Countergambit with the extra attacking move <code>h4</code>,</p>

<pre><code>[FEN ""]
[Title "Reversed Albin"]
[Startply "12"]

1. h4 d5 2. d4 c5 3. e4 dxe4 4. d5
</code></pre>

<p>but according to my database this has actually never happened in a real game, so I might be mistaken.</p>

<p>The book <em>Groteske Schacheröffnungen: Wagnis mit Methode</em> (1991, in German) by Stefan Bücher has a chapter about <code>1. h4</code>. </p>
 13055: <p>Apart from the fact that you can develop your rooks (which <strong>isn't good</strong> so early in the opening, because your rooks might become vulnerable), the only other "benefit" I can think of is that <code>a4</code> (more likely than <code>h4</code>) can be useful after some transposition to a normal opening, e.g. stopping black from playing <code>b5</code>.</p>

<p>That being said, black can comfortably choose (thanks to your gift of a tempo) an opening where <code>a4</code> is useless.</p>

<p>The other move <code>1. h4</code> is even more problematic because castling kingside is much more frequent than castling queenside and <code>h4</code> weakens the pawn shield in front of your king.</p>

<hr>

<p>So I don't think it's worth calling these possibilities benefits at all.</p>
 13012: <p>1.a3 is a semi-respectable opening called Anderssen's Opening, and since he beat Paul Morphy(<a href="http://www.chessgames.com/perl/chessgame?gid=1019048" rel="nofollow noreferrer">http://www.chessgames.com/perl/chessgame?gid=1019048</a>) with it, it cant be so ridiculous. He used it to enter an English opening or a reversed Sicilian. I think Larsen once did the same.</p>

<p>There is at least one trap. Black plays a reversed Scotch 1.a3 e5,2.e4 Nf6, 3.Nc3 d5, 4eXd Nxd4 5. Qh5. This move is playable, and very lively, on the fourth move of the regular Scotch, but it's not played much because of 5. Ndb5 which is not available here.</p>

<p>Beginners would probably disapprove of 1.a3, on the grounds that it does not give them enough freedom of action to put their Rook en prise.</p>
