- Traveller - my first encounter with a non-class-and-level system after a couple of years of D&D. It was a very different approach and opened up my eyes to new possibilities.
- Champions - Point-based character creation! Superpowers! A mechanical framework for every object in the universe! Opposition built on the same rules as the PCs! This whole game was a revelation and is still a very different approach than most RPG's
- James Bond 007 - A unified task resolution chart was a huge innovation, one that would show up in a more popular game (Marvel Super Heroes) the following year. Figuring out how that fit into the game and how damned useful it was made this game even more fun.
Also: Hero points! This is the first RPG I know of where players had a pool of points for their character that could be used to adjust die rolls on the fly. It fit the genre perfectly - after all, a 00 doesn't miss that critical shot! The GM had a similar system of points for villains. This kind of "bad roll insurance" mechanic took a while to really take off but you find something similar in a whole bunch of games nowadays.
- Shadowrun - The whole system was amazing. I have Unarmed Combat 6 and I am fighting a guy with Unarmed Combat 4. That means I roll 6 dice with a target number of 4, and my opponent rolls 4 dice with a target number of 6 - genius! How simple is that to keep track of?! Non-opposed checks have a target number, typically a 4. The whole game works like that! Now the math can be strange, and figuring probabilities can be tough, but as far as intuitive mechanics it was great and at the time we loved it. There was very little book-checking for normal stuff and that's a huge win even today.
- 3rd Edition D&D - while the unified mechanics got all of the attention that had been done before as far back as the 70's in everything from RuneQuest to Traveller. Feats were just Champions Advantages. The big innovation to me was per-level multiclassing. This took what had been a fairly restrictive class and level system and turned it into a modular Lego-style system where a player could build exactly the character they wanted as the levels piled up - regular classes, prestige classes, and racial levels all combined to make for a very cool and very flexible set of mechanics for creating a character. It's not quite Hero System in flexibility but it's closer than one might think.
- Savage Worlds - The first RPG I can recall that was expressly built with playability as the top concern. It's a radical change from the prior Deadlands system which was very very crunchy and detail-oriented. Savage Worlds chucked all of that and started rating stats and skills in dice - not number of dice (ala Star Wars or Shadowrun) but type of dice. The "Wild Die" a bonus d6, separates important characters from mooks. Target number is always a 4, with a few potential modifiers, bonus effects for exceeding the target by certain increments, and the occasional exploding die. A Savage Worlds character will never have the kind of detail found in a Pathfinder character, but they will have more mechanical differences and details than a Fate character. It's a system with a nice balance of speed and simplicity while still generating interesting outcomes.
Additionally, the game uses cards for initiative. Instead of rolling a die players draw a card. This doesn't seem like much of a change but it opens up some interesting mechanical options beyond just "who has the higher number" and adding or subtracting bonuses. First, you have a suit and a color in addition to a ranking and some effects can key off of one or more of those. Similarly, the two jokers trigger certain effects as well. Also, things that impact a character's speed or capability in an action situation can be reflected in having them draw more or fewer cards, having them choose the higher or lower card, or letting them use multiple cards in a single round. Some people might look at the cards as just a quirky difference of the system but they can be a lot more.
- D&D 4th edition - Taunt mechanics! There were powers in the game that inflicted penalties or even damage on a target if it attacked anyone other than you! This is a surprisingly powerful thing and really does open up the option for a "tank" type character approach.
Next, certain classes had the ability to lock down enemy movement as a built-in capability. When you can stop an enemy from moving on their own turn it opens up a lot of tactical options. This also added to the "tank" concept described above and seriously increased the importance of the "Attack of Opportunity" by inflicting a consequence other than straight damage. I miss this ability in other games, from Pathfinder to 5th Edition.
Finally, the entire concept of forced movement of other characters: Many powers in 4E involve moving another character away from another (a "push"), or pulling them towards another (a "pull"), or moving them at the acting player's discretion (a "slide") and it really changes up combat from a relatively simple exchange of damage to a far more dynamic affair. A pull could represent anything from an insult that strikes home and enrages the target into charging the taunter to a magical tractor beam to an entangling tentacle. A push might be anything from a magical force effect to a mighty punch. Superhero games tend to have some kind of knockback mechanic, but the only game that even comes close to accommodating some of these kinds effects is Champions, and even then it typically happens only on a character's acting turn, not as an interruption or a reaction on another character's turn.
All of these innovations made a combat round in 4E far different than any other RPG combat round I have played. Just because it's "your" turn doesn't mean you're the only one that will be doing something. It's a full-table interactive process and it is a blast when running at full speed. It does mean that combat takes a while sometimes, but people have had the same complaint about Champions for years and you know what - it's worth it! If you want "crunchy" combat, where every move matters, this is a great system.
- Marvel Heroic Roleplaying - a radically different approach in mechanics for ... everything - especially when it comes to a superhero game and the way those have been traditionally handled. There's a little bit of other games from Fate to Savage Worlds but the system as a whole is not like anything else out there. One description was that it's an exercise in justification and building dice pools, so it rewards both understanding a character and a player's ability to think on their feet. On top of the innovative approach, it manages to balance Hulk and Hawkeye to where both can contribute equally well to a team, something that is tough to do in a lot of other games. Plus, it a) works in actual play and b) is a lot of fun in actual play and c) requires very little book-lookup, another strongly favorable aspect of these mechanics, especially for a superhero game.
- D&D 5th Edition - Advantage/Disadvantage. Such a simple concept! Such a simple mechanic! Now everyone can be a 4th Edition Avenger! One of my players ran an Avenger in 4th edition so I have seen the power of "roll twice take the highest" when applied on a large scale and it is great. It can wipe out a large number of modifiers - instead of a bonus or penalty for certain actions or circumstances you have advantage or disadvantage. It's a great example of innovation that improves a game in every way.