Title says it all. Feel free to add comment, theory, or explanation.
Just to clarify, this is only regarding turn 1 of White, and no proceeding turns after it.
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Houdini 1.5 on my old machine (1.8 G 2 cpu) slows down a lot around 20 ply (10 moves).
At 20 ply, it seems to slightly favor a four knights queen pawn game, starting with d4 or Nf3 over the Four Knights (1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6)
it switches at 22 ply to the Ruy Lopez Berlin (1.e4 e5 2.Nf3 Nc6 3.Bb5 Nf6 4.O-O Be7).
at ply 23, it switches back to d-pawn four knights, but starting with 1.Nf3
None - yet.
Brute Force is a pretty well defined problem solving technique that consists of checking each and every candidate for whether it is a solution. Since we are starting at move 1, a candidate has to be defined as a complete game of chess and the only possible objective criterion for its evaluation is whether it forces a win for white or not. No engine has analyzed a forced win for white from move 1 so far, so no actual brute-force engine has reached a conclusion yet.
As soon as you introduce a heuristic (or multiple ones like positional advantage, material advantage, space advantage...) for evaluating partial solutions (game positions that are not a checkmate yet) and their distance to a complete solution, like all chess engines do, it stops being a brute-force engine. Those evaluation techniques are the reason why chess engines are able to choose moves at all until the whole space of possible chess games is solved and/or a force win for white is found (which I think is highly unlikely).
Thus, my answer is that there are no brute-force engines in use today - if there were one it would still be thinking. Yes, brute-force might be used to describe the basic technique that modern heuristics developed from, but the evaluation criteria are actually a lot more important for an engine's capabilities. To put it bluntly, calling todays chess engines 'brute-force' is akin to calling a house a 'hole-thing', just because you need to dig a hole for the foundation. The rest is much more important and interesting.
I hope you, dear reader, will not take this as nit-picking on words, but as an addendum to the actual answers already given by other people. They answer the spirit of the question, this one... just the semantics - there was nothing else left to answer. :)
A chess engine works by trying to "rate" positions, and evaluate how strong they are. It could find a checkmate in 4 moves (that one where white checkmates by getting queen to f7 (IIRC)) but it'd be stupid to consider this "AHA! My evaluation is that I have won!" As such it is very subjective as it depends hugely on what it thinks the opponents best move is.
It is for this reason it is not (read: I really really doubt, with my mathsy-background) known if chess is a fair game, that is will "perfect" playing by both sides lead to a draw, or white or black to win, because that "perfect" part is so subjective.
With 0s and Xs, it is a fair game because it is easy to show that "perfect" playing leads to a draw.
It gives an overview of what Houdini suggests for the first few moves for White (and also Black).
Figured I'd post the famous Deep Blue vs Kasparov games.
Game # White Black Result Opening Comment 1 Deep Blue Kasparov 1–0 e4 c5 2 Kasparov Deep Blue 1–0 Nf3 d5 3 Deep Blue Kasparov ½–½ e4 c5 Draw by mutual agreement 4 Kasparov Deep Blue ½–½ Nf3 d5 Draw by mutual agreement 5 Deep Blue Kasparov 0–1 e4 e5 Kasparov offered a draw after the 23rd move. 6 Kasparov Deep Blue 1–0 Nf3 d5 Result: Kasparov–Deep Blue: 4–2 Game # White Black Result Opening Comment 1 Kasparov Deep Blue 1–0 Nf3 d5 2 Deep Blue Kasparov 1–0 e4 e5 3 Kasparov Deep Blue ½–½ d3 e5 Draw by mutual agreement 4 Deep Blue Kasparov ½–½ e4 c6 Draw by mutual agreement 5 Kasparov Deep Blue ½–½ Nf3 d5 Draw by mutual agreement 6 Deep Blue Kasparov 1–0 e4 c6 Result: Deep Blue–Kasparov: 3½–2½
e4 c5 = 1-0-1
e4 c6 = 1-0-1
e4 e5 = 1-1-0
Nf3 d5 = 3-2-0
d3 e5 = 0-1-0