Does it strike anybody else as odd that I have an easier time against Charizard than I do Bowser? Definitely a Pokemon I would learn if he were his own character. Anyway, we all know he's got a death grab on Ness and that it doesn't really help when you fight against him. You're better off taking him to stages that have transformations. I remember fighting this really good Pokemon Trainer recently named Buuda. I think it was him that I was fighting and I took him to Castle Siege and he tried to death grab me there, but the transformation saved me more than enough times.
Ness' aerials are obviously better than Charizard's. Because Charizard is a heavy character, Ness can easily combo him. PK Fire is okay against Charizard. I'm sure they can DI out of it easier than Bowser, but I feel that the attack is still effective against Charizard. Little damage is better than no damage, I suppose. If you get Charizard off the stage, don't be afraid to use PK Thunder. Just spam the heck out of that attack until he returns to the stage. If you feel like it, I guess you could go for a dair spike or whatever attack you feel is necessary at that time.
When fighting Charizard, you've got to watch out for his Rock Smash and his fair. One launches debris and the other shoots ember, which obviously do a bit amount of damage. If you're close enough to Charizard and you get hit by that Rock Smash, it does a lot of damage, so that's one thing to look out for. Charizard's got some nasty smash attacks, too. I'm not sure how early his f-smash kills, but it might kill around the double digits, I'm not sure.
When you're recovering back to the stage, do your best to be above or at mid level of the stage. If you're below stage level, you'll either get dair spiked or they'll use Flamethrower to try and keep you from coming back. That's all I have for now, I guess.