When designing a game, there are several ways of approach. There no such thing as the one and only approach, in practice you will use several approaches in combination, without one 'leading' approach. The games I have come up with so far always started from a theme rather than a mechanic, like "wouldn't it be nice to have a game about... "
Top down versus bottom up design
Top-down means, you have a game concept / a theme / an atmosphere in mind and you start detailing the mechanics, look-and-feel, etc. Bottom-up in this context means, you identified the mechanics you want to use, maybe most of the look and feel and work you way up to a concept, a kind of trial and error or interactive design: you have an idea how the game in the end should look like, but have not figured out how it all fits together, actually you try to build a game around the details.
Game Architecture versus Game Patterns
Architectural design and Pattern design, as methodologies, are borrowed from IT-approaches. The relate a bit to top-down/bottom up approach and as such the combination top-down/architecture and bottom-up/pattern are closely linked.
In architectural design, you start with defining the game-principles, the conceptual phase. Then you go into the logical phase where link the principles and last but not least you go to the operational phase where you fill in the details (boards design, etc.).
Pattern design is closely linked to architectural design, what you do is, you copy most of the architectural principles of an existing game and customize the logical and operation parts.
The most simple and fast way to design a game is based on pattern approach: you take any game, change the goal, the theme and look&feel and there you go. Want to design a game in five minutes? Here is how you do it: take 'Mensch argere dich nicht' / Parcheesi, add pitfalls, add chance cards, change the board layout and change the pawns-models into frogs and last but not least think of a challenging name: there you go! What you actually did is, you started of a existing game, changed / added some mechanics, changed the look and feel and gave it another name. Lets call this 'copy-development'.
If you look at the many games published (especially the ones based on hypes (Pokemon, Big Brother, TV shows, etc.), you will find that all these games were developed around existing mechanics and actually developed by 'copy-development'.
Developing according to architectural design does not guarantee, you won't end up with a look-alike of an existing game, but in general the game will be more consistent and refreshing, especially since you might end up with a new mechanic (not necessarily a good one though).
Building on themes
Another approach is building on themes / atmospheres. This means you don't have anything than just the idea to build a game based on a theme. Typical examples are the various TV-games / Movie-games. The only thing you have are the characters and some of their characteristics you want to show in the game.
Many games are based on themes, espcially wargame scenario's.
Copying the Wheel (vs re-inventing)
For something completely different: most of the great games (Scrabble, Chess, Risk, Mah Jong, etc.) don't have a specific theme, they are generic (and unique) in their mechanics and field-of-play. They are relatively easy to learn and offer the user various roles (aggressive, defensive, cooperative (in multiplayer / team situations), etc. Also, don't try to reinvent these games, many other people will do that for you (I know of at least 4 chess variants sold commercially and I probably can come up with 10+ commercially sold variants of trivial pursuit (non of them very successfully though, unless marketed in specific niche markets (like sports))). It is not hard to come up with a another Games-Workshop-alike game either. The hard thing is to come up with something new, a completely new theme (haven't seen those lately), a complete new mechanic (Magic the Gathering), a complete new marketing concept (WotC), etc., which actually can lead to new spin-offs.
The last you want to do is 'improve' a classical game ('I have reinvented Chess: you win if you capture the Queen': maybe you're right, but you have to convince a few million people). Even when your name is Bobby Fisher, former World champion Chess, introducing 'Shuffle Chess' (randomizing the pieces on the 1st row and mirroring them to the 8th row) is not something the world is waiting for (introduced in 1992). Should I mention Mega Chess, Stealth Chess (actually a combination between Chess and Stratego!), Tile Chess, global chess (see picture), 3-D Chess then? Probably not, you got my point I guess. I must admit though, some of the variants are pretty interesting. Nightmare Chess by Bruno Faidutti however is very funny add-on.
Doing it the simple way
Should I give more examples of variations on great games to prove my point that these are quite useless (esp. in a commercial sense)? Neeeeh. Nevertheless some useless examples:
More examples: doing it the simple way
Get a license to use the name 'Harry Potter'. Call the game 'Harry Potter to the Rescue' and make up a story of Harry Potter rescueing someone. Rename the chance cards to 'Harry Potter looks around, move 3 tiles back', 'Harry Potter falls asleep, miss next turn, 'Harry Potter learn a new spell, take another turn', whatever comes to your mind. Add some good looking graphics to the board and the cards, replace simple pawns by 'Harry Potter' lookalikes and there you go: a Blockbuster!
By the time Harry Potter is 'out', do a 'Find and Replace' and replace 'Harry Potter' by some other popular figure.
First of all, if your game has a theme, make sure that you have already some idea about the tokes, the board, etc. A color printer really helps. A hobby shop nearby is handy, especially if they have loads of small things that can help representing stuff (little pieces of wood, shiny things, etc.). A toyshop for children also come in handy when it comes to tokens and stuff (remember those small wooden animals?). As the example above ('doing it the simple way') shows, Theme and Look&Feel are crucial to the game. The prototype should at least give some impression of that!
When designing a game, you should consider the many tools that can help you, in your creative phase, in your designing phase, in your alpha & beta phase and in your first demo phase (No, I won't mention PC's, printers, scissors, paper, etc...).