Now, I'm not sure how popular this series is here. I personally love the TimeSplitters series, it is my 3rd favourite video game franchise (after Final Fantasy and Super Smash Bros.), and I waited so long for TimeSplitters 4, however I know now that it will never happen.
A little history for me before I state my opinion. My first experience with the series was at my uncle's house, when I saw my cousins playing that game. I ended up getting his PS2, however, for some reason I never played the game. Fast forward to Christmas 2009, when I get my second PS2 from another uncle (my first PS2 broke in 2007) with a copy of TimeSplitters: Future Perfect. I fell in love with the game's quirkyness, and played it for hours. It didn't take too long before it surpassed 007: NightFire as my favourite First-Person-Shooter, which I admit I am not normally a fan of. I played the multiplayer with friends and family, which I almost never do.
In around March-April 2010, my friend gave me back the copy of the original TimeSplitters (I gave it to him after my PS2 broke), and we played that game for hours, mainly the story mode. Looking back, I can't believe that I never played it when I originally owned it. The game was much more of a challenge than the original, but it was just as addicting. In fact, it surpassed Future Perfect in my favourite FPS game.
I searched forever for a copy of TimeSplitters 2, and it take me years before I could find one in a thrift store in the Summer of 2013 (which seems weird, considering that it's the best selling in the franchise), and I played it quite a bit when I got the chance. I haven't played it as much as the others, so I will reserve my judgement on where it goes.
However, I would say that my favourite is the original. I know that most people would disagree, so I would like to see your opinion on it.