Computer chess was made famous by the victory of IBM's Deeper Blue over Kasparov, the ex-world champion.
The game table looked like this:
A marginal victory but enough to make the world believe that computers had finally become better chess players than humans. Why did it happen? There were four main reasons:
Point four is the most important and needs a little explanation. In the original match (Kasparov vs. Deep Blue which Kasparov won) the object was to create a computer which could play chess as well as possible. IBM described it as an experiment and the atmosphere was friendly. In the rematch the objective had changed; now IBM had set out to create a computer which could beat Gary Kasparov at chess. IBM is alleged to have said that it would give printouts of Deep Blue's calculations to the chief arbiter but it later changed its mind and refused to hand over these documents. It was no longer an experiment. It was a contest which saw IBM using every means at its disposal to defeat Kasparov. If a major corporation like IBM points its almost limitless resources at defeating a single individual it is almost inevitable that that individual will be defeated. The computer was designed with Kasparov in mind. With Kasparov's love of open positions the team created a computer whose horizon in open positions would exceed that of Kasparov, psychologically forcing him to play in a somewhat artificial "anti computer" style, one which does not suit him. Kasparov's style of play is not well suited to playing against computers of any kind but especially not ones whose abilities include 200,000,000 position evaluations per second! (A horizon is the ply limit of a person's or more usually a computer's calculations). As Kasparov pointed out in the press conference afterwards, if Deeper Blue were to be entered into major tournaments it would be "torn to shreds". Computers have an unavoidable style because of their unchanging evaluation functions, (the programming which lets them decide how good a position is). In such a short match it was difficult to learn much about the computers style but in open tournaments people would grow accustomed to its play and would adapt - in a way which computers cannot - to it's style. Also, computers cannot search selectively. (Well, they can, but when they do they risk ruling out the calculation of variations in which they obtain "long term compensation" for material, which weakens them somewhat). This means that Deeper Blue probably had to calculate a great many variations to a full 14 plys deep, (7 full moves). If deeper blue were able to play against positional masters from the past, Capablanca or Staunton for example, then it might have struggled to 'understand' the marginal differences between the positions it would be thrown into. It might be argued then, that Deep Blue did not become better than mankind at chess but only better than a particular individual who it was designed to be able to beat.
However, there was more bad news for humankind in December of 2006 when Kramnik (who was then the world champion) lost 4-2 playing against the computer program 'Deep Fritz'. Unlike Deeper Blue, Deep Fritz was a commercially available program which was not designed with Kramnik specifically in mind. Kramnik was a very high class positional player and if he couldn't beat the machine, it's unlikely anyone else would have been able to either. Hence, it now seems clear that computers have reached the stage where they play better chess than humans and all the positional skill in the world isn't enough to fight off these tactical monsters.
How to beat chess computers
There are a number of standard ways of beating chess computers. However, they are less effective against the newest programs. Never the less, they are still probably the best try for anyone below master level.
Attempt 1. Slow kingside attack. Adopting an opening such as the Stonewall and then gradually massing your forces on the kingside can be very effective. You must be careful to use an unusual move order as the newest programs will play too well against the standard move order using their 'books'.
Attempt 2. Keep it closed. One way to do this is to play a slow double fianchetto system with pawns on a2 b3 c2 d3 e3 f2 g3 and h2. Then wait for the right moment to break with c4 or f4. You MUST hold these breaks back as long as you can! Let the computer drift as it lacks any concrete tactics.
Attempt 3. Play positionally. This is only really viable if you are a naturally positional player. If you are such a player, do what you normally do. If you are not, don't even try it. Imposing a style you don't have on your own play is usually disastrous.
Attempt 4. Turn off the computer. This is the most effective method. You should wait until you have played 1. e4 and then turn off your computer. You should then adjudicate the position as better for white and award yourself the win or else claim victory by default.
Commercially available chess computers
There are many portable and tabletop chess computers available, most of which are fairly weak. You get what you pay for and with tabletops and handhelds you are paying for the hardware as well as the software. If you pay less than $100 the chances are that you will end up with an unchallenging opponent. If you want a serious opponent you need to be looking at the $100+ range. If the computer has an Elo of less than 2000 it's probably not going to help your chess a great deal. If you have a PC and your first concern is with the strength of the opponent you are purchasing then you should probably just buy some chess software and run it on your PC (Fritz, Rybka, Shredder, and possibly Chess Genius, are [in my opinion] the strongest programs available but you can download a very strong free chess program called "crafty" [and a GUI for it to run 'under' called winboard] from the web which is probably stronger than any commercially available dedicated chess computer [i.e. any tabletop or portable]). I ought to mention that companies trying to sell you tabletop and handheld chess computers often say "you should consider buying a better model, one which is considerably stronger than you, as it can always be told to play more weakly if you find it too strong, and as you improve as a player you can let it play more strongly rather than having to buy a new machine". This is true, but it is most unsatisfying to win against the machine if you know it's not doing it's best and so people generally do not use this option very often. Also, technological progress means that the prices of the strongest models fall over time. Thus it might turn out that it would be cheaper to buy a weaker model while you are a beginner and then buy a stronger model as you become stronger than to buy the top of the range model in the beginning. It is also likely that the top of the range model you would have bought to start with would be weaker than the one available a few years later when you need a sterner challenge. I realise that this advice is a bit vague, but the key thing to remember is that you usually get what you pay for.
I have always been impressed by the Mephisto line of desktop chess computers but if you are looking for a serious challange then I would advise against getting anything weaker than the Milano Pro. The strongest model they offer (as I write this) is the Atlanta. It claims to be around 2200 to 2250 Elo and will offer any opponent a decent game. The top of the range Novag products aren't half bad either.
If on the other hand you are looking for a something to give you a friendly game from time to time and don't mind the computer playing some weak moves here and there then any chess computer made by a reputable company is likely to serve you well. For example, the Excalibur Chess Station is relatively cheap and very versatile.