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.

If I recall correctly, what you are planning to do may violate the ToC set but if you still insist, Apple's website highlights the following restrictions:

Your Apple ID can have up to 10 devices and computers (combined) associated with it. Each computer must also be authorized using the same Apple ID. Once a device or computer is associated with your Apple ID, you cannot associate that device or computer with another Apple ID for 90 days.

(Note you still have to Authorize all computers you are planning to sync from - so they count in the ten device limit as well as each iOS device).

Here is the relevant quote:

(i) You may download and sync an App Store Product for personal, noncommercial use on any iOS Device you own or control.

The legal definition of control is vague for what your particular use is, but you are more likely to end up limiting your number of registered devices on your Apple ID if used incorrectly

"Downloading for free" of purchased apps by another person is certainly not something Apple would like. You can technically do that, however you have to also let his device sync to your iTunes library and let him use your Apple ID and password each time he needs to update the installed apps in this way. In short: your friends' device must be considered by apple as one of your devices.