Both of the comments by looper and Krazer are correct, and they tell pretty much the whole story. As of episode 658, Ash (Satoshi) is 10 years old, the same age he was when he began his journey. However, based on reasonable assumptions for how often the Pokemon leagues meet, he should have aged at least 5 years.
The strongest indication that time has passed is probably the short from the 3rd movie, Pikachu and Pichu. What Ash says implies very strongly that they've been together for at least a year:
Don't you know what today is, Pikachu? This is the day we first met. The day we first became friends. I think that's pretty special, don't you?
There are a few other instances where the passage of time is referenced in the anime. In Episode 063, Ash says in the dub that it's been a year since they last visited Viridian City. In the original, Satoshi just said that it's been a long time. Also, in Episode 469, Team Rocket says they've been chasing Pikachu as long as Dawn's been alive, which would be 10 years. That's probably better interpreted as breaking the 4th wall, since the anime had been running for 10 years at that point. There may be other instances, but the fact that a lot of time has passed since the first episode is indisputable.
This is one of the most glaring plot-holes in the anime, though it's understandable why the writers don't want Ash to age. Presumably it could send problematic messages if Ash were 20 years old when he first started travelling with 10-year-old Dawn (or Iris, though I don't know her age), though it's honestly still problematic if he's 10 years old. Of course, Pokemon is marketed to children, so having a 10-year-old protagonist is also better than having someone at least 15.
However, there isn't any official explanation for this. The writers have never answered why Ash and the other characters aren't aging even as time passes. In my opinion it's best just to regard this as a plot hole and ignore it as much as possible. There are some fan theories for why Ash wouldn't age even as time passes, but honestly they're a little bit Farfetch'd, if you know what I mean.