Here's my $0.02
Travis Barker is a decent drummer. He's got some unique fills, interesting ideas for licks. I think by far his best work was in Boxcar Racer. If you listen to "Watch The World", his opening snare part shows he's got decent marching chops (nothing spectacular, of course) and the lick he plays during the verses is kinda neat. "Sorrow" also has a cool groove, as well as "All Systems Go". As far as his work for the Transplants goes, "Killafornia" has a funky little latin groove going on, and "Hit The Fence" has a cool drumline-esque beat which caught my attention pretty quickly.
I've been playing for two years, and I can play most of his stuff, but I wouldn't say I've got him down pat. Compared to other pro-level drummers, he's not much but for the aspiring drummer, he's got some licks and fills that would for the most part draw inspiration. He's creative, energetic, has fast hands, and a good feel for the music. He's not exactly the 'model' drummer.. I think he's got too much of the "hotshot" mindset, but personally.. his stuff intrigues me, and I enjoy both listening to the bands he's in and learning and playing his beats.
You may not like his persona, the genre of music he plays, or the attention he draws from the mainstream.. but admit it, the kid can play.