Is Behting Study Still Beating Computers? This is the famous Behting study, first published in the magazine Bohemia in 1906, which is often used as a demonstration that computers can’t solve all positions.
White to move and draw with a very elegant move.
Spoiler:

 1. Kc6!! g1=Q 2. Nxh4 Qh1+ 3. Nhf3

Question is, is this study still beating engines?
Clarification: Suggesting best move, doesn't mean engine understands(or finds) the solution. Without evaluating it 0.00 or =/=, it doesn't mean it's solved. Actually, best move with -4.** means engine believes that best possible continuation for White is this move, with winning advantage for Black.
Imagine you ask a question to someone about a chess position in which White has a move which is the best and draws. You ask, which move is the best and why, and you get an answer like this: &quot;Best chance is this move, but even if it's White's best chance, it looks losing&quot;. And you know that move draws. Would you accept this answer as correct answer? Definitely no.
I recommend to read:

A very instructive article about interpreting evaluations of chess engines: How to Read Engine Evaluations?
This post: Computer evaluations: How trustworthy are they?

Notes about edits: As the question turned into a discussion about whether the position solved by engines or not, I revised the question accordingly.
This question is totally about facts, and not opinion based. Some of the answers are opinion-based, but it's not the problem of the question. It's terribly wrong to close this question, instead of letting people discuss it.
For the record, the soundness of the Behting study has been under a cloud for some time because it is not easy to refute 1 Ng7+ Kg5 2 Nf3+ Kg4 3 Kf5 h3 4 Ke4 g1Q 5 Nxh6+ Kh5 6 Nxg1 h2 7 Nf3 h1Q 8 Nf5 "etc.", but according to recent analysis by GM John Nunn (2012) the study is sound after all.

It should be feasible for a chess engine to reach a 0.00 evaluation because there are only a few thousand drawing positions that need to be evaluated (depending on wK/bQ position, with or without the c/d pawns), and once the search has exhausted that space they'll all evaluate to a draw.

Here's a similar challenge:

[Title "NDE 1986 (2nd Prize, Israel Ring 1986)"]
[fen "5k2/1n6/1p3K2/P7/1P2N3/p1P2B2/8/2b5 w - - 0 0"]


White to move and draw.

Solution:


   1 a6 a2 2 axb7 Bf4 3 Ng5! Bb8! (a1Q 4 Ne6+ Kg8! 5 Nxf4 Qxc3+ 6 Kf5 and Black can't win; 3 . . . Bd6 4 Ne6+ Kg8 5 Nc7! Bxc7 6 Bc4+ draws.  So the Bishop crosses the critical square c7, which however White can exploit too:) 4 Nh7+! Ke8 5 Bc6+ Kd8 6 Ng5 Kc7 7 b5! a1Q (Kd6!? 8 Ne4+ Kc7 9 Ng5 repeating) 8 Nf7! positional draw.