I only recently got DuckTales Remastered on Steam, but I really like what I played of it!
Another one I have very fond memories of is Barnyard on Wii, based on the animated movie (which later became a tv show. That counts, right?). I won't say anything about the movie, but the game is actually pretty darn good! It may be a little bland for adults, but I think it's a perfect entry into open-world mission-based gaming for kids. Fun and challenging missions, but not too challenging. A fun overworld to explore that's not too big, and a fun narrative to keep kids going. I loved it as a kid, and I highly recommend it for any kid if you can find it cheaply at a yard sale.
I also really love Viva Piñata: Pocket Paradise, which I thought was based on a cartoon, but apparently the cartoon is based on an Xbox game, so it doesn't count.
