How can I find out what software I've bought in the App Store?

How can I find out what software I've bought in the App Store?

I'm Using my iPhone 3G and haven't backup it as frequently as I should and
would like to know what software I've bought for it. So I know I don't
have to pay for it again. Yes I can try and buy the software but I want to
know of all the apps I've bought.
I know some apps wont be available for my old iPhone but they will work if
I buy a new one. I need to know how much money I will lose in Apps I can't
use anymore. If I buy a new phone that isn't an iPhone.
So How can I find out what Apps I've bought for my iPhone. I have both
Windows and Mac computers available.