LOVED the Timesplitters series! =) Unfortunately Free Radical who developed the games has since gone bust which is a shame as there WAS a 4th Timesplitters game planned. I can't think of many shooters since which have matched its arcadey style, most shooters these days strive towards realism. All I can think of to recommend is the Bioshock series. It's a lot darker in tone to Timesplitters which at times was somewhat light-hearted and humorous, but it's got a great supernatural storyline, eccentric characters and most importantly solid gameplay and pacing. Bioshock 2 also has a decent online multiplayer mode which is reminiscent to that of TS2. You can find both games pretty cheap here on Amazon. Hope this helps.
I'm enjoying "Brink" which doesn't have the same sense of humour as Timesplitters but has similar goofy character design, and never lets logic or plot get in the way of back-to-basics shoot 'em up fun (like changing your skill-set mid session, which makes no sense at all).