As a straight male: Always make the offer. It's just polite to your date. If she wants to pay that's fine, but its never a bad thing to have offered to help someone.
AccursedTheory said:
Me. I demand it.
It's what my mother and father taught me.
Best of intentions here, but I'm pretty sure the wrong approach. Take it with a grain of salt but:
NEVER DEMAND IT. It can come across creepy and even a bit controlling. If she wants to pay for her own meal/movie/etc., forcing her to not pay can make her (and honestly anyone else) think...
A.) This guy isn't even listening to me and isn't respecting what I want.
or
B.) Wow, he's seriously telling me what to do with my money?
Oldest dating advice in the world: If you're not sure what to do, pretend its a friend of the same gender you're just being nice too.
"Hey, I got this."
"Oh don't worry about it. I got it."
"Yeah?"
"Yeah."
"All right."
Addendum: Her birthday/Your anniversary/Any major relationship event? You take that check. You take it and you fortify it and you use all manner of warfare and skullduggery to get your card to the waiter first.