Many types of games rely heavily on a well-crafted world, be it imaginary or partially based on reality. Some obviously will need richer environments than others; classic role-playing games are much more narrative-driven than, say, sports or shooter titles.
In any case, designing your game's world can be a critical part of crafting a valuable and entertaining experience for your players. There are a number of things to keep in mind when setting out on this journey. If you keep the following tricks in mind during the process, the results should speak for themselves.
Take More Than A Day
As the old saying goes, Rome was not sketched on a napkin in a bar. Or something like that. Anyways, the point here is that good design takes a lot of time, effort, and refinement. The first step to creating a great experience is to be prepared to invest a good deal of work.
The all-important corollary to this is that your first version is probably not worth keeping completely as-is. Get feedback, sleep on it, and iterate. Many of the best stories took endless tweaking and even complete rewriting before they became the classics we think of now.
Originality is Dead
There's a dirty secret to the creative process: very few ideas are truly new. Virtually everything is derivative in some way or another. This isn't as much of a problem as it may sound like; putting a fresh spin on something is often all it takes to invent a really compelling idea.
Clever world-crafters will use this to their advantage. Instead of striving to fabricate a completely new experience, work on adding your own flavor to something that people will already find familiar. This is powerful because it gives you a common ground with your players right off the bat. That commonality can be a highly effective hook for getting someone into the experience to begin with. Dropping into a completely alien setting can be stimulating for some types of player, but most will be overwhelmed and confused. Give your players just enough familiarity to know what to try, and they'll be encouraged to explore on their own.
Go With What Grabs You
The most surefire way to create a boring experience is to not care. Creating a world is an immense and involved task; to do it well requires a degree of passion and fixation. Even if your personal "hook" is just a phrase or mental image, start with a seed that you find compelling.
It's worth keeping in mind that not everyone will find the same things equally enticing; knowing your audience can be immensely valuable in crafting a world that appeals to them. However, you need a concept that is personally important to you.
Having a key idea or even sensation you want to convey will take you far. You probably only need a few words to express this in most cases, but handled well, it can become a thread woven deeply into the fabric of an entire universe. Players will sense your personal attachment to that thread and will tend to be intrigued themselves.
Retelling personal experiences can be a great way to accomplish this, but don't feel constrained to actual facts. Dress up the story in the way you wish it had turned out, or raise the stakes. If you saved the day by showing up to the family barbeque with the ketchup everyone else forgot, turn that into a grand adventure with a runaway nuclear reactor and the emergency shutdown codes that nobody else could find.
The flip side of this is that sometimes you need to be less attached to an idea; if something grabs you but nobody else seems to care, it may be time to make the difficult decision to leave that idea behind and pursue something else. Even the best creators struggle with this; the difference between extremely good storytellers and tabloid article authors is that the good world-crafters are willing to let go of stupid ideas.
Learn From the Masters
Developing your skills as a world-builder will follow the pattern of any other discipline. Studying the work of other creators will be vital to honing your own abilities.
Draw insipiration from things you've read, watched, played, or even lived through. Think about what kinds of feelings are evoked by your favorite stories and worlds. Think about what sorts of emotional reactions you want to instill in your players.
Remember what your favorite experiences and worlds feel like, and think critically about how they may have accomplished that ambiance.
Use Every Art Form Available
Games - and especially video games - have the fascinating advantage of being multimedia products. The word is rather beaten to death in today's society, but it's worth going back to the literal definition: games span many different mediums, from visual art to audio to music and maybe even physical feedback.
Never underestimate the potential of this when crafting your own worlds. A game's visual style, audio style, musical style, and so on can all be used to great effect when applied in concert. Know how to leverage the various stimuli you have at your disposal, and use them to help underscore the emotional impact you want your world to have.
Know When to Break Expectations
A powerful way to create emotional tension and memorable moments is to break expectations. When players think they know how something will turn out, and the tables suddenly turn on them, the resulting moment of shock can be a powerful tool for instilling certain impressions. Just be sure you know what reaction you want to go for; arbitrarily breaking expectations is just plain confusing. Using shock as a tool to reinforce impressions must be done judiciously and carefully.
Feed Imagination; Generate Curiosity
There is a classic rule from improv comedy that applies to developing your worlds: never say "no." In other words, try not to purposefully close off possibilities. Leave things open for imagination and curiosity as much as possible, unless you need to resolve a major plot point - but even then, open questions can be powerfully compelling.
Imagination-feeders can be as simple as strange symbols in obscure locations, or as massive as giant spaceships appearing in the night sky. The extent and scope will depend a lot on the world you want to make, but the principles are timeless.
Purpose, Interest, Resistance, Resolution
The final cornerstone of crafting a compelling world is a storytelling pattern as old as stories themselves. The general idea has been studied and documented for centuries, but it bears repeating with a minor twist in the context of creating game worlds.
Put simply, players must be taken through four stages of dramatic progression, beginning with purpose. Purpose gives players a reason to be in the world and a goal to accomplish.
Once the player's purpose is established, and usually hot on the heels of that moment, it is time to create interest. Give the player some motivation beyond simply "get this random thing done." Another way to think of this is that interest is the context in which purpose plays out.
Of course, dramatic tension cannot exist without resistance. There must be some person, force, internal conflict, or other general reason why the purpose is difficult to achieve. The nature of resistance is usually bound up heavily in the interest.
Finally, once the player overcomes the resistance and accomplishes the purpose, they should feel a sense of resolution - that something was indeed changed, perhaps for the better (or maybe not!) in the course of exploring the game world.
The trick to all this lies in layering and staggering the stages of the cycle. An overarching story line may set up the four phases on a grand scale, while a single "mission" or "chapter" does so on a slightly smaller scale, and then a single battle or adventure within the game may provide a third and most-succinct incarnation of the pattern. Virtually all game stories follow this structure to some degree.
Putting It All Together
Find something that interests you personally, and build around it; be prepared to invest a lot of time getting it right and fleshing out the details, and never lose sight of the possibility that you may need to start over. Along the way, use examples from other experiences you've found compelling to help inspire and shape your own world. Never close off possibilities if you don't absolutely have to, and feed the imagination of your players - even if they imagine things you never thought of yourself; or maybe especially if they do.
Last but not least, know how to structure the dramatic cycle of your world, and don't be afraid to break expectations to underscore your points and create lasting memorable moments.
Once you've created a universe, you're officially qualified to make an apple pie from scratch. Best of luck!