There's nothing particularly noteworthy about turning 34, save that I can now say that I outlived Jesus (in your face, Jesus). There's not even any interesting numerology. Two years ago when I turned 25 on 5/25/2005, now that was cool. But it's pretty much downhill from there.
In the year after turning 16 my brain underwent one more set of (I assume developmental) changes, and then after that it just stopped, such that today I still feel like a teenager, it's just that I hold a job and own a house and walk around in a 34 year-old's body. At some point after that I realized why people get so freaked out turning 30, then turning 40, and so on. The internal them stops getting older while their outside face, and the outside world, just keeps on keeping on.
It's the little secret of the world, that it's entirely populated and run by 16 year olds; 16 year olds who are still caught up with who likes whom, who's popular and who isn't; we hurt and do hurt to each other like 16 year olds. It looks different, sure, but it's only because we don't have those faces any longer.