I think what helps them most is that the characters are toys, but you can relate to them better than the people in the story. In the first film, Pixar did a great job showing us an emotion that everyone has experienced in their lives before, jealousy of a new person. Be it on your block, in your school, work, etc. Everyone has experienced it, and the way they handled the emotions of the characters was spot on.
The graphics have aged a bit since they originally came out, but not so much that it looks dated. The details of the humans have improved dramatically from the first and second film which was a nice touch, since the second one had more human scenes.
The story of the second one was not as good as the first in my opinion because it lacked the emotional connection that the first one had. It was there, but less common, and not everyone could connect with the feelings that Woody was feeling, left out and lost. Maybe they can, but it lacked the wide appeal the first film had. It did have more action in the second film, which was a nice change, but I felt that the characters weren't as interesting the second time around.
Despite this, I still think these movies are worth seeing. And am looking forward to the third one as well.