Out of the anime I watched as a child, this is the one that stuck with me. I think the reason this series had such an impact on me, and still does, is that even now it still holds up as a pretty solid anime, especially for a kids' show. A lot more care was put into the story and characters than in the other seasons of Digimon, or something like Pokemon.
The story of Digimon Tamers diverges from the pattern of Digimon Adventure and Digimon Adventure 02, in that it takes place mostly in the real world, and not in the digital world. It has done away with the first 2 seasons; it takes place in a universe where they only existed as a TV show and some children's games. The story is separated into several arcs that run together quite nicely. It starts off with a sort of monster of the week format, but each episode contributes something to the characters' development, and there are some that deal with an ominous government agency that provides the series with some rather dark atmosphere. Once the show gets to the digital world, things become a little more complicated, and the climax presents us with an exciting and satisfying conclusion.
This series deals a lot in the relationship between parents and children, and the plot involves the parents fairly often as well. Kids lying to their parents and parents lying to their kids is something you'll see often. This, I think, helps to set it apart from other kids' anime, like Pokemon or the earlier seasons of Digimon, which can be seen, on occasion, trying to provide a good message for children. Digimon Tamers is not a show with a moral for kids to pick up; rather, it's tellling its story while staying appropriate for a child audience.
That said, the need to remain appropriate for children, combined with the fact that the creators were ordered to advertise the card game in this show, does tend to hold the story back a little. Still, I think it's a good story that some people will really enjoy.
The characters are one of the most important parts of this show. In the earlier seasons of Digimon, we got fun but ultimately stereotypical characters whose backstories were only lightly touched upon, and who only learned very simple lessons over the course of the show. Not so with Digimon Tamers; the size of the main cast has been cut down from previous seasons to only three main characters, making use of the show's length to add new characters when appropriate. This allows it to really go into the main characters' backstories, how they got to be the way they are, and what problems they have to face because of it. As stated before, this is not limited to the child characters. The adults play a significant role in this as well; by the end, they're almost as important as the main characters. The Digimon themselves receive the same treatment. If there were any reason to watch this show, it would be to see how the characters operate over its course.
The animation is nothing spectacular, but is above average. The action scenes between Digimon look good, and you can tell that special care went into the scenes that were particularly climactic; there are a couple of rather epic moments that the art and animation are able to capture really well. If I had a complaint, it would be that a few of the Digivolution sequences make use of pretty awkward CG.
The sound is the same as the animation; not great, but more than adequate. It contributes at the right moments. Unlike the animation, it doesn't have the possibility of suffering from bad-looking CG.
I am enamored with this show, I make no effort to hide it. I'm a big Digimon fan, but this is the series of Digimon I've rewatched the most, and the only one I still watch. I would recommend this to anyone, though I understand that not everyone has the time for a 51 episode kids show. If you're a fan of sci-fi, or character-centric anime, you would probably like it.