VLC for iPad and iPhone is available, but how to install it? (it is not an App Store app)
VLC was available on the iTunes App Store for some time, and the process for installing it was like any other.
However, a developer, who has contributed to VLC development in the past (IIRC) got in contact with Apple and asked VLC to be removed due to License Incompatibility.
VLC is licensed GPLv2, which states among many other things, that the source must be available, and I believe there are other provisions surrounding VLC with regard to Apple's per-device DRM.
Thus, Apple de-listed VLC from the App Store, and you cannot buy it anymore. Note that those who purchased it before will likely have it forever. (I still do, I still use it!)
There are two ways to install it/run it today:
(1) If you have a paid Apple Developer account, you may take the source, import it into XCode, codesign it, build/deploy it onto your own device. (Or for that matter, get someone with a Developer Account to do it for you.)
(2) Since VLC ships a raw .app file, it can be installed if your iPhone/iPad/iPod is jailbroken. I believe raw .app files can be installed via Installous? (Anyone is free to correct me on this, as I don't use Jailbroken devices anymore.)
Update: VLC for iOS was subsequently relicensed and re-released on the App Store. It can be downloaded by visiting this link.