I actually understood the basic rules for Yu-Gi-Oh! by just watching the series for a few years. They basically explained the rules in the early episodes in season one, even though that season didn't really have the right rules for summoning monsters. Anyway, I didn't get into the video games, the only means that I play the card game, until last spring. As for Bakugan, most people, including myself, couldn't really understand how the heck to play the game.
At least with Yu-Gi-Oh!, despite the lack of rules in season one, the first episode did give you at least a decent idea of how the game was played. It takes the rules for Bakugan a while longer to sink in and I still find it confusing at times.
As for the first Yu-Gi-Oh! anime, I actually wasn't impressed with it. I thought the first few episodes were interesting since it was something new. But by the time they were about half-way through the series, I was actually growing tired of how Yami Yugi's other self would defeat the villian of the week in that week's game. It didn't help that they gave Mio a main character role, despite the fact that she was there for only a couple of chapters, pretty much only to give Honda a comedy relief gag and the fact that they were focused on different games didn't really grap me either. It was like they focused on even the most simple games. While I haven't read all seven volumes, and I really should really all of the volumes one of these days, I thought what I read from the first two or three volumes of the manga was done much better than the first anime series.