I've been 39 for a couple of days now and can't say I feel any changes from being 38. 'Course it doesn't usually sink in that I've had a birthday until the first time I have to answer the "How old are you?" question. And I've done this enough times to know that you don't magically feel differently just because a particular day of the year came and went.
At least not after you pass 25 or so. Younger than that and each birthday seems special somehow. I think it's because there are so many milestones when you're younger: starting school, hitting double digits, becoming a teenager, driving, high school, etc. After you hit 25 the only thing that's left is just endless years of aging; all the fun stuff's already happened. At least from the perspective of someone under 25, obviously.
I suppose I need to make this year memorable somehow though, as it's my final year in my 30's. I'll see what I can come up with.