Snarf's Inarguable List of Top 10 Most Influential TTRPGs!
The following is a product of maths and logicks, and cannot be reasonable disputed. Other than #1, they are not listed in order of importance.
1. D&D. (1974)
OD&D (the Little Brown Books) started the industry as we know it.
2. Amber Diceless Roeplying. (1991)
I am not going to argue that it was the first diceless RPG (people were playing freeform D&D the year after it was released). But ADRPG was the first real commercial salvo for diceless RPGs.
3. Fudge. (1992)
A clean break from the increasingly sclerotic RPGs of the '80s, Fudge was flexible and light, and presaged important later innovations (eventually becoming FATE).
4. Paranoia. (1984)
Not just a comedic masterpiece, this was the first meta-RPG. While we now associate it with comedy and The Computer, Paranoia was actually a very clever satire and parody of the rules and tropes of other TTRPGs that said a lot about what "RPGs" were in the '80s.
5. Ghostbusters. (1986)
Dice pools start here. Heck, love it or hate it, the d6 system was born from the game. I still remember the first time I ran it.
6. Runequest. (1978)
Not just a good game in and of itself, it introduced Glorantha and formed the basis for the later Basic Role-Playing System and Call of Cthulhu.
7. Apocalypse World. (2010)
The first game that used the Powered by the Apocalypse system, Vicent Baker's "story-first" game has had a lasting impact since its debut. This also let to Blades in the Dark and the Forged in the Dark system.
8. Lasers & Feelings. (2013)
I'm giving L&F the nod here as the game that kickstarted the "lite rules" revolution. Not every game has to be less than three pages - but this started the process of asking, "Why not?"
9. Traveller. (1977)
In the '70s, most RPGs were either D&D, house rules of D&D (including the first superhero game) or games that were like D&D, but with different rules. Traveller was NOT D&D, and many of its innovations in gaming and design were incorporated into later RPGs.
10. Castles & Crusades. (2004)
The first "OSR" game and the beginning of a movement that started with attempts to retro clone OD&D and 1e rules, and eventually grew to include games that had completely different mechanics but were trying to emulate the "feel" of older games (Electric Bastionland).