YES, you can use your puchased Apps on your girlfriends iPhone. If you are using two computers (yours & girlfriends) then BOTH need to have YOUR account on each and both need to be authorized with your account. Your girlfriend CANNOT use any other account or she will pay again. As stated above, you can do this on up to 5 computers.
When you are on HER computer and click on the purchase button of the App that you have already purchased, IT WILL ASK "Are you sure you want to purchase this App?" click yes, it will then say you have already purchased do you wish to down load again. Select yes and you will now have two for the price of one.
Again, make sure that she is on YOUR account and authorized or you will pay again.
My wife and I do this all the time with a classic and 3G iPhone
Good Luck