Apple have an "App Store" which is the sole way of installing third party applications on onto their devices (short of jail breaking them and installing a custom firmware). Using it requires iTunes and an Apple ID, and if you naively go into the iTunes store with an existing Apple ID and try to activate it for use in the store then it also requires valid credit card be provided. (If you try to use the AppStore application on the portable device with an Apple ID that hasn't been activated for the iTunes Store then you get a generic error message; if you try to use it in the iTunes application you get channeled into providing a credit card.)
Since I'm wary of allow auto-billing of my credit card based on some other credentials (even before the App Store was hacked), I'd avoided the App Store completely and just used the built in applications (which mostly worked fine, as I'd chosen my device such that the built in applications covered almost all of the things I wanted to do).
However there are a lot of free App Store applications, and some of them are even useful. So it was a bit annoying that I couldn't even get the free applications without providing a credit card. Eventually there was a free App that I was a bit more determined to get, and I persisted long enough to find a way to get Free Apps from the App Store without a credit card. To do this you must create a new Apple ID just for the App Store, as it appears impossible to use this technique with an existing Apple ID for no obvious reason (well, other than the necessary option being missing).
The approach (mostly as provided by Apple):
Start iTunes, go to the "iTunes Store" section, make sure you're not signed in (since you have to make a new account), go to the "App Store" tab.
Find a free application (there are lots of them).
Click on the "Free" to "purchase" it
Since you are not signed in, you'll get a prompt to either "Create new Account" or sign in with an existing Apple ID. You must choose "Create new Account" (irrespective of how many other Apple IDs you have; AFAICT if you try to use an existing Apple ID you'll be forced to provide credit card details).
You'll be taken to the iTunes store signup, choose "Continue".
You'll be presented with half a dozen or so lengthy legal contracts to read and agree to, and have to tick the "I have read and agree to the iTunes Terms and Conditions and Apple's Privacy Policy" checkbox before clicking "Continue". (Don't bother with the "Printable Version" link as Apple appears unable to maintain a working link to their own web site in their own application -- you get a 404 -- you have to find the "printable version" on their website starting with Apple Legal. The benefit of reading it all is dubious since one of the terms is that Apple can change the contract at any time.)
Enter email address, password, lame challenge/response verification, date of birth (sigh) and be sure to opt out of the spam at the bottom of the page, then click "Continue". (You probably have to have a different email address from any other Apple ID, but fortunately the Internet provides ample means to getting multiple email addresses; I just used another one on my vanity domain. To complete the process you do have to be able to receive email from the App Store with a validation code in it, so it needs to be a working email address at least when you are signing up.)
The next page is "Payment Method". If you followed the above directions (and it appears only if you followed the above directions) you get an additional option: "None". Be sure to select the radio box "None" rather than entering any credit card details. You'll have to fill in most of the address details in order to proceed, even though it appears there's really no need for Apple to have them in order for you to use the App Store (sigh). When done, click "Continue".
You'll get a page telling you that an email has been sent to the email address that you provided, with a link needed to activate the new account. Wait for that email.
When the email from the App Store arrives, go to that link in your web browser. It'll push you content that wants to auto-open in iTunes and you need to allow it to open in iTunes.
You'll be prompted to log into the iTunes Store with your new Apple ID, and you should do so.
You get a page telling you that your iTunes Store Account has been created.
In "only 12 easy steps" you now have an iTunes Store Account which has no credit card associated which you can use to "purchase" free things.
Ironically the free App that you tried to purchase to trigger that process is not purchased as part of the account creation; if you actually wanted that particularly thing you have to find it again and click on "Free" again, while signed in with your newly created account, in order to actually get it. Then ensure it's been downloaded (there's a Downloads section which apppears), then go to the section for your device and "Apply" the downloads to the device.
(In theory it should now be possible to use the AppStore application on the portable device to get free Apps directly using the newly created account, but I've not yet verified that.)