A game's true impact can't really be judged until a good several years after the initial launch. You can usually anticipate certain titles that will leave the biggest legacies, but it's only when you see a repetition of their mechanics and themes across the years, that you can look back on them and say 'Ah, so that is where it all started'.
'Influence' is obviously a pretty broad word, and in this context can mean anything from a game's effect on the tone or gameplay of later games, to their visibility in the wider culture. Sometimes an influential game might not even have others emulate it, simply because it came to completely dominate and define its genre. Or maybe a great game had an impact that seemed like a great thing at the time, but ended up tainting the medium anyway... like Michael Bay did with Hollywood.
Now that we're over five years beyond the 2000s, we can look back on the decade with enough distance to judge the biggest movers and shakers so far, and how they - for both better and worse - redefined the industry in their own way.
12. Uncharted 2: Among Thieves
The original Uncharted was a wonderful - if overlooked - early game for the PS3, still testing out the capabilities of the console and giving us snippets of the wonderful and witty writing that would go on to shape the series.
But with the sequel - announced in spectacular fashion by that helicopter gunfight sequence in Nepal at E3 - Naughty Dog upped the ante tenfold. The graphics were breathtaking, the action sequences spectacular and the expert pacing set a blueprint for subsequent action-adventures to try and replicate. Uncharted 2 was a milestone for video game storytelling, adeptly flowing between cutscenes, action, and expository gameplay where you'd be in control, strolling through a temple or a town while the characters interacted with each other.
Since then, Uncharted 2 has arguably only been topped by Naughty Dog's very own The Last of Us, using the mechanics of the medium to create memorable stories that are interwoven expertly into the gameplay itself, rather than simply looking to Hollywood for inspiration.