In my point of view;
In the first seasons, Ash had this character to be the youngest, and not so experienced. The height marked that impression of his character, but didn't determine his age, only character. It was confirmed in The Battle Of The Badge, that it was one year ago since they were in Viridian City last, therefore at least telling us that they're one year older.
Then if you calculate the many times they've said that they've been travelling for two months, three weeks, a couple of days, and so on, it'll give a slight impression on when they reach their next age mark. Also proving that time does go by in the anime.
Now if you look at Ash when he ended his journey in Johto, and started his new jounrey in Hoenn, you can clearly see that his physical features have changed drastically since he started his journey in Kanto. He's more muscular, more tanned, taller than May, who's supposed to be ten. Although May was taller than Ash when they first met, but considering that Gary used to be taller than him, and they're the same age, then the height can't really determine that.
But Ash soon got shown to be taller, and it also shows in comparision with Brock. Before, Ash's head just reached the top of Brock's shoulders, but now he's clearly taller than that. Guess the growing sprout finally kicked in :p
Ash's attitude towards certain things has also changed. Remember the Mudkip episode where they met the guy, with the funny hair? Ash clearly acted unexpected towards him, and that shows that he's getting that attitude that certain teens have. Some preteens also have that attitude though.
But Ash is more out going, but also more aggresive. His patience towards Team Rocket has shortened greatly, and he pretty much hates being near them now. Although in some occasions he can team up with them, but that's only in extreme situations, where there are no other options.
Thatwas just to point out that Ash has indeed changed greatly throughout the time. Just compare a picture of him when he started his jounrey in Kanto, with a picture of him in Johto, and then a picture of him in Hoenn. You'll clearly see that his features are different in each picture. Heck, just compare a Kanto pic of him with a Hoenn pic then you'll see a drastic difference.
From what I could tell from what they've said about time in the anime, and in the change of features, I'll have to say that Ash is about 13-14 years old now. I can't really use his height as an example since it's different to each person. But I can use the fact that his physical features don't really fit a preteen in my opinion. 14 seems to fit pretty well.
That was my rant. ^^