Okay, this is going to be me all intellectual and pretentious as if I know what I'm talking about. Man I love balloons. I have no idea why.
Let's dissect video games. It's going to be bloody, so get on your hockey mask and prime the chainsaw.
Where to start? I had this idea the other day. All "leveling" and general character progression in video games can be classified as belonging to one of two axis. Either lateral development or vertical, or in more useful terms either skill expansion or skill refinement. It's a fine point in most cases, but it helps understand the mechanics at play. Let's explain by example.
A game heavy on skill expansion is the Legend of Zelda titles. Link doesn't spend a lot of time getting "better". There is some of that - more powerful swords and more hearts - but this is not the driving mechanic. It gives the game a pretty low difficulty curve, since you can never ignore "weaker" enemies, although your ability to survive them remains. You never gain real mastery. Okay, having described the opposite of what I intended, here's my point. The games revolve around lateral movement - instead of getting better or stronger, Link spends most of his time broadening his skill set. He gains abilities like that of ranged attack, but manoeuvrability bonuses feature heavily - iron boots, hookshots, deku leaves. This opens up more and more of the world, giving a kind of exploration mastery rather than combative. Often these abilities play into combat, but selectively, and often as what amounts to a secondary effect. The player is encouraged to use these devices imaginatively, and the absolute greatest example of this is the wind waker and deku leaf combo. By angling the wind correctly, and finding the right ledge, you could explore areas of the land that looked completely inaccessible. Blind corners were rare but present, encouraging an observant eye especially. As another example, take bombs. By any other game's standard, bombs are an essential offensive tool! But in LoZ they're very unwieldy, impractical except in very specific circumstances that make even their few actual combat applications more a matter of strategy than power. Mostly, however, they are used to explore, and the observant Zelda player (particularly in the earlier games) could find a myriad of treasures. This is the essence of lateral movement. You were gaining new abilities that applied in a range of circumstances, and were (almost) never made obsolete or supplanted. People often jokingly criticise the dozens of items Link totes around, but nearly all of them take on an essential character.
On the other end of the spectrum you have the Pokemon games (okay this is nintendo heavy, sue me!) which deal almost exclusively in vertical movement. Let me once again back up and explain what lateral movement they have. The HMs. Poorly implemented at times, they serve the same function as Link's boomerang. But most of the time the only "obstacle" (besides being heavily scripted) is level. How strong are your abilities? Even most moves are simply replacements of older ones - ember becomes flamethrower, scratch to slash, tail whip to screech. If you cannot enter an area (and survive) it's typically a matter of not being strong enough, not of not having the wrong abilities as it would be in LoZ.
You'll notice that neither of my examples are perfectly dedicated towards one or the other. That's because it's very difficult to construct one dedicated to just one system of movement. Imagine link with only three hearts, or Pokemon with no HMs . Both are doable, but you'd have to significantly alter the games to fit around these absences to the point it'd be rather awkward - you'd need to make Pokemon even more heavily scripted, creating random obstacles like the man standing outside of Mewtwo's dungeon in Red & Blue. To use an entirely non-video-game example, Dungeons & Dragons balances these two nearly perfectly. You're mostly concerned with increasing your chosen skills and occasionally your abilities, but feats are giving you more abilities and special features, as well as class features that, being dependent on level up, blur vertical and lateral movement.
What does this all mean? It means that you can help set your game's tone based off of which type of movement you're concerned with. Lateral games are great for exploration, allowing you to hide things behind item-specific blockades. You can make a vertical-based exploration game, like Fallout 3, but you'll never make a puzzle game of the same caliber. Also Fallout 3 is a soft vertical-based game, as it levels the game to the player. Quests will always contain some vertical growth, however, as this establishes the challenge the game provides, usually from a combat standpoint. The final fantasy games showcase this - by the end of the game, your level 80 guys are fighting extraplanar demons, and this just wouldn't be acceptable in a lateral-based game without some mechanic (*cough* triforce) that explains (circumvents) this discrepancy between apparent ableness between fighter and enemy.
I forgot the point I was making. Hope this is interesting.