If I make a new Apple account will I keep other data?

I want to create a new Apple ID account on my iPhone 4, but I have games with data such as plants vs. Zombies and clash of clans and stuff like that. If I make a new account on the App Store will it delete the data and progress I have on these games?

Not on the phone but the data will not be saved to your icloud to restore from since the app and icloud are from the same account they are linked and will only work with each other and no other Apple ID.

My recommendation try recovering your password. Call up Apple if need be.

If you don't delete it from your phone, it won't.