How to download bought apps without old credit card?
Once you purchased an app, you can always re-download that app free of charge, given that the following criteria are true:


The app is still offered on the App Store
The app is available in your country


If you moved countries and all the above is true for you, apps purchased elsewhere will be hidden, but can still be obtained by regularly searching for them.

They will state a price and you will need to go through the purchase process again, but once you entered the Apple ID you used to purchase the app originally, you WILL receive a message saying that you already own it and that the download will be free of charge.

I know that this sounds scary and I always shiver until I receive that message myself, but having moved countries myself, I can confirm that behavior and never had any problems re-downloading an app (except for sometimes finding them among the many other search results when looking for it).

One thing, however, since you mentioned Aperture and iPhoto.  Since Apple is discontinuing those apps, if you want to keep them, re-download them very soon and make a copy (e.g. compress them) to store somewhere on your computer.