The Legend of ZeldaIn A Link to the Past, abilities come in the form of tools that are found along the journey. These tools/abilities are not just for variety of play, they are also the keys to unlocking areas of the map. The first barriers are bushes that block you from going anywhere except the castle (which has the sword that can cut bushes). Then it's rocks that can't be lifted without the glove.
Pros: This provides very hard gating mechanism for limiting player freedom, without them feeling like they're being limited. Every barrier feels like a puzzle to be solved.
Cons: Excessive quantities of items that are only good in specific locations are just glorified keys to locks. For example the cape could have been worked into a gameplay mechanic, but instead its only required for one barrier (Maybe two? It's been years since I played it last). Same deal with the invincibility cane.
Legend of ManaNow technically this game has levels, but they were largely irrelevant. LoM has an ability system that allows you to bind any four abilities simultaneously. You start with a handful of abilities and as you use combinations of abilities, such as crouch and jump, you unlock new abilities such as high-jump. The game also paces the content by requiring the discovery of artifacts to open new areas.
Pros: Increased play diversity. The new ability can replace the two old abilities for convenience and to free up buttons for other abilities. Or, the player can hang onto the old abilities if they want to decide at the peak of the jump whether to kick, strike, or just land on the ground. This gives the player more options for customization, but doesn't do too much too fast.
With the artifact system, which has multiple quests per location, plot can be hard gated by only providing the plot continuation artifact when the previous plot event has been completed.
Cons: You may have to use a FAQ to discover some of the rarer combinations of abilities. This system only works for derivative abilities; completely new abilities need to be introduced via some other mechanism.
Super MetroidThe system used in Metroid 3 is basically the Zelda way, except that the abilities are more versatile and gating isn't as strict. Most notably about Metroid 3 is the ways that advanced players can work around specific items for speed runs or minimalist completion runs (I believe the record is 14% item collection).
Pros: Every item has uses beyond overcoming a specific obstacle. The grappling beam is used as a hard gate for entrance to the wrecked ship but there are plenty of places where grappling just helps you get around faster and is up to the player to use. For example, doing a really tricky wall jump off of a single wall then up and around a ledge can get you the wave beam ahead of schedule.
Cons: This kind of freedom can be hard to do with a complicated plot. Metroid gets around this by having a plot that is mostly back story revealed by the environment. There are only two plot events that are gated: the into and the ending.