Can I use my Apple ID to download apps I've purchased onto a friend's iOS device?
If you choose to do so, your friend will not be able to update apps without knowing your password. If you give your friend your password, they will then be able to shop for apps using your account.  The other problem is that your friend may not be able to sync with his/her computer without erasing the apps.

The last problem is Apple restricts each Apple ID to a fixed number of devices in a rolling window. At the moment, I believe you generally get frozen after 10 devices in a short time. I was setting up a deployment of 100 iPads using iCloud backups, and we hit a 90 day freeze for that account after 10 devices hit the App Store. We didn't care about updating apps - the end users were to delete these free apps once training was completed and part of the training was for them to make their own accounts and re-download the things we "staged" for initial training.