In my past experience the presentation of the flower is key. Don't just hand her the flower and say "Here". You need to dazzle her. Leave it beside her pillow before she wakes up, on her desk at work, or someplace she would least expect to find flowers from her boyfriend on her birthday.
Make sure that you give her the flowers earlier on in the day too. You don't want her to think it was a last minute idea just before dinner time.
As far as for the type of flowers to get her, try prying it out of her. Find out if she has a favorite. It may be something rare or something very common. Most girls seem to really love orchids though. They look beautiful and show that you really gave it thought.
You can either get a nice orchid arrangement at your local florist or another great idea is to get an orchid that is planted in a nice pot so that she can not only enjoy getting flowers, but also she will be able to enjoy it for more than just two or three days.
I hope this was helpful. Good luck wowing your girlfriend on her special day!