From Bulbapedia, the community-driven Pokémon encyclopedia.
The aging of characters in the anime has been a subject of common fan debate, since it is not addressed by the anime itself. The passage of time is clear, but characters show small, if any, signs of aging, despite openly saying that years have passed. The writers and character designs seem to ignore the issue of aging, usually so the viewers of the show feel closer to the protagonists. It is easier for a child to relate to a ten year old rather than a twenty year old.
To be safe, on Bulbapedia, characters are referred to as their age at their first appearance, if it is indicated.
One common theory is that, like in many cartoons, the characters never age and are trapped at the age of their first appearance. However, this seems strange since the passage of time is pointed out every once in a while without the mention of any character's birthday. It is even more questionable that the anime has directly pointed out years of time passing. One of the most common supports for this theory is that Ash and May are supposedly the same age when May begins her journey, even though Ash has traveled through three regions and competed in their leagues before she received her first Pokémon. This is also the case when Dawn starts her journey, as she is the same age as Ash, though he has been through five regions this time (including Kanto twice). This is easier to believe in the Japanese version, where all characters have retained mostly the same voice. However, in the English dub, many characters have had their voice change over time, especially Ash, who's voice has become noticably deeper over the seasons.
Another common theory is that, because only one half-hour episode airs approximately each week, the flow of time in the anime is considerably slower than in real life. This theory is supported by the apparent, though minimal, growth of the characters, as well as the noted marks of time. The common estimate is that three real years translates to one year in the anime. However, this theory still faces the same problems as the Eternal Youth theory.