The only way to download US Apps is to set up a new US iTunes account. Sounds simple, doesn't it, but it isn't as easy as you think.
The problem is setting up a payment method, as whatever payment method you set your account up with really needs a US address for verification.
I'm not an iTunes expert in any way, but the way I did it was:
Sign out of your current (Dutch) iTunes account, you will then get an option to create a new account.
You can then set up a new account (new e-mail login) and choose USA as your country, and just use any US address (made up ones are fine, just make sure you use a valid ZIP code).
You will next get to the section where you set up your payment details. Here is where it gets a bit tricky. I tried 6 different (UK) based credit cards, with all manner of combinations of addresses, but none of them would work, so what I did was this:
You can get free promo codes on this site, and one of the plus (or minus points, depending on how you view them) is that these promo codes only work on a US iTunes account. But you can use this promo code as your initial payment set up. I can't remember the exact bit you click on on the payment setup page (it might be, redeem code, or select payment option later, and it take you to a screen where you can enter the promo code). I'm sure you can work it out from the payment setup page.
Anyway, once you have done this, you will have set up your US iTunes account, and you can switch between your Dutch account and US account simply by signing out and signing in again with whichever login you want to use.
However, in your US account, you now have the problem with funding your purchases, as although you have set your US account up (using your free promo code), you still haven't set up any paymnet method to purchase apps.
The only way I have found to fund this is to purchase US iTunes gift cards. I usually pick one up in the US whilst I am out there (I usually go out once/twice per year and pick up a $25 iTunes gift card whilst I am there). You can then simply use the Redeem option in iTunes and redeem yout US iTunes gift card, and this will apply the credit to your account, and negate the need to have any sort of credit card on file.
You can also get US iTunes gift cards (quite easily, but at a premium) on various sites or Ebay, or maybe someone on these forums who is based in the US can help you out.
Anyway, once you have your US apps installed into your US iTunes accounts, you can simply sync your iPhone to iTunes and it will sync all of your apps to your iPhone (both US and Dutch).
Best of luck,
Kevin.
