Most of my favourite games, such as Diplomacy, have little or no element of luck - either via dice rolls, hands dealt, or other methods.
What other games can you recommend that rely on 'skill' alone?
One game per answer, game name formatted as header and link to more information. Vote for your favourite if it exits already.
Go is an ancient game; at least 2500 years old, and possibly as old as 4500 or more. Originally from China, it is now most popular, and professionally played, in China, Japan, and Korea, though there are strong and growing amateur communities in Europe and the Americas.
Go is a simple, pure abstract strategy game, with no element of luck or hidden information. The rules are quire short and simple; the simplest expression of the basic rules is 10 sentences long, though rules that cover a few extra conventions for ending the game sooner and making scoring easier, and provide more detailed explanation, are a little longer.
Despite the simplicity of the rules, it is extremely strategically deep.
The starting player has a slight advantage in Go, which would give a slight luck-based advantage to who goes first, but because winning is based on total territory scored, you can even that advantage out by giving the second player a few extra points; generally somewhere between 5 and 8 extra points, with the number having drifted upwards a little in recent years as people have discovered that the original amount was still a bit too low.
One of the great features about Go is that it allows you to play handicapped games against strong or weaker players. By letting one player start with a few extra stones on the board, you can even out a difference in skill, and still have an interesting game even though one player is considerably stronger than the other. This is great for small clubs or tournaments, when you don't have enough players of roughly equal level to compete against each other; instead you can play handicap games, and everyone has a chance to win while playing at their own skill level.
Go is a beautiful game, with a great balance between whole board strategy and local tactical battles. It has been studied deeply for centuries, and new innovative ways of playing are always being discovered. In recent years, mathematical analysis of the endgame using the theory of surreal numbers has yielded insights that have helped even top professional players, who have devoted their life to learning the game, and have teacher lineages going back hundreds of years.
I could wax poetic about Go for hours, so I'll stop here, and invite you to check it out. The Wikipedia article gives a good overview, while Sensei's Library is a wiki devoted to Go. There are hundreds of books on Go, a manga and anime series about it, professional players and teachers, schools devoted to teaching young Go players, servers for online play, Go clubs all over the place, and more.
Is an obvious and longstanding game of skill alone.
Stratego may seem like a slightly strange choice since each game involves a completely a hidden setup, but it's a setup entirely devised by the opponent with distinct strategies, counter-strategies and bluffs available. If there's an element of luck it's in trying to guess your opponent's approach to a setup, but there are no dice rolls for combat or drawing of positions involved. First-move advantage is also minimal, and certainly seems less important than in chess.
I can't say that there is no luck element at all in Puerto Rico, but it is definitely extremely low. The game involves selecting roles to perform actions. Each person will perform the chosen action, but the actual chooser gets a bonus for it. The main theme is developing plantations to grow crops, and then shipping these goods off for victory points. The only luck elements I can see in the game are the 5 random crops that are available to plant during a planting phase, and possibly the turn order. If you the skill level of the people playing is drastically different, then sometimes the person you are sitting next to and what role they choose can greatly affect your strategy.
In the same vein as Checkers, but popular and distinct enough I felt it warranted its own post.
The initial board position is fixed, pieces to be played are controlled, and the object is to have more of your color upright than the other player.
There's a style of game that Chess belongs to, as Jon already suggested, to which Go and Shogi and Checkers and Halma also belong. Modern family members are Khet and ZÈRTZ and I think most other members of the GIPF project. These games have in common that, other than in Diplomacy where you have the written orders, all information is openly visible - except of course the secret plans plotted by your opponent. They are also all fairly abstract games, in that they do not pretend to model any aspect of the real world.
Homeworlds is an Icehouse game about space conquest. In the multi-player game, there is hidden information about who is good and who is evil, and thus there is a certain element of luck in your guess about who is who. In the two player game, however, there is no luck; it is a pure abstract strategy game.
To quote Andy Looney on Homeworlds:
I really like John Cooper's Icehouse game, Homeworlds. I think it's one of the very best Icehouse games we currently have. It's elegant and exciting, it looks great on the table, it's different every time, the theme rocks, and it makes excellent use of the pyramids. One of my criteria for a perfect Icehouse game is that it offer deep strategy while using little or no equipment other than the pyramids, especially including using the table itself as a featureless gameboard. Homeworlds is a perfect Icehouse game.
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Where Chess is an abstract pure strategy game representing medieval warfare between kings, Homeworlds is an abstract pure strategy game representing interstellar warfare between planets. In both games, complicated forces have been reduced to elegant icons, but where Chess is played on a restrictive, 64-square grid, Homeworlds creates a free-form, dynamic space-map out of any plain surface.
Whereas Chess was a game played by Renaissance Kings, Homeworlds is a game for Starship Captains.
The only random element within Caylus is the initial 6 buildings setup order. The rest of the game is pure skill. As with the Endeavor answer, there is a very very small advantage that may be had by going first with order of the buildings, but I think this adds more variety and skill to the game rather than luck.
The object is to get four of your color in a row horizontally, vertically, or diagonally. No luck - just pure skill against the other player.
No luck at all, just plain skill.
Seeing as Brian added Go, I'll get ahead of him on Icehouse for once. A turnless game of pure skill and diplomacy. (Also consider IceTowers and Zendo, which use the same pieces.)
I suppose it could be argued that a first guess that is "right" would be lucky, but it should be a game of logic based upon guesses leading to a pattern match against the hidden sequence of pegs setup by the other player.
Like Blokus, no luck; an advantage to going first (more so than in Blokus), but a great game of strategy with simple rules but very interesting consequences.
To my knowledge the game has only 1 random event - flipping the Westeros cards. This randomness can be nearly entlrely removed via the optional "Westeros Phase" rule variant in the A Clash of Kings expansion (which allows you to see the results of the random card flip several turns in advance).
Aside from the Westeros cards, everything is based on player skill. Games regularly feature numerous epic staredowns and healthy backstabbing.
This game is based on Diplomacy (and in my opinion is much better). If you like Diplomacy you will probably love this one.
I also prefer games that have little to no randomness. One of the best ones I've come across lately is Endeavor. Other than the initial tile distribution (which isn't tremendously significant, just changes it up a bit), there's no randomness at all. One of my favorite games right now.
The only luck element is the initial distribution of goods, but it's shared by everybody equally and I think it helps replayability. Also the initial turn order used to auction the real first turn order. After that it's all there on the table, no more luck!
Age of Steam has much more luck, with semi-random goods going to the cities during the game.
Besides the ones already mentioned:
I've never played it myself, but it's supposedly more complex than chess is, though it probably suffers from the first turn advantage issue.
fits the bill it is very chess like
I actually prefer it to chess because, although it is simpler in many ways, each player has the ability to move their opponents pieces making some interesting strategies possible.
Mancala has no luck. Some might debate that if you are using irregular sized pieces and don't keep strict track of how many stones are in each space there is luck in picking the right space to "move". However I'm not sure that applies, as it is simply a matter of counting to keep track the quantities of stone and the entire game state...
Maharaja has no random elements.
A deduction game that uses cards, but they have small impact on the game, since you usually have plays that will be useful, and when you don't you can trade them all in.
It's got a great diversity of initial setups, but once the game starts there's no chance at all.
An unusual 2-player dungeon-crawl game. Some luck in the initial setup (the board is random), but pure skill once the game starts. Looks like Descent, but plays nothing like it - it's a game of positional advantage and smart maneuver. Has a simple and effective handicap system - which is needed, as experience pays off in a big way.
Wargame reimagined by boardgame designers! Combat involves absolutely no luck: Two attackers will clean out any enemy piece, no questions asked.
There is one small element of luck though: The tide, which impacts the board layout. However as long as you keep your weather-predicting piece, you know the tide for the next turn, so this mitigates luck down to almost nothing.