It depends on where you are, and what situation you are in. For example, if you are on a date and there is an awquard silence, then the best thing to do is to ask him about his day, or something that you can both relate to. Don't ask him something you have no interst in.
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It's really not about what you ask him. It's more about listening when he answers. Just remember, most people like to talk about themselves. Always find out how much common ground you have-i.e. music, movies, books, etc.-and go from there.
Well me and my boyfriend play this game called Have You... I always go first... ask "have you..." then a question... Its very fun!
YOU CAN ASK HER WHAT HAVE SHE BEEN DOIN. WHAT TYPE OF PET DO SHE HAVE. WHAT DO SHE WONT TO BE WHEN SHE GET OLDER.
Ask her how many relationships she's been in, ask her what all her "favorites" are, ask her how long you think your relationship will last... be creative