You can use the "File Sharing" feature of various apps THROUGH iTunes, but without having to actually SYNC with iTunes.
Install the free CineXPlayer app. This will allow you to play a much broader range of videos.
Then plug your ipad into any computer with iTunes installed. iTunes will recognize the device, and let you browse it WITHOUT syncing it. If you go to the "Apps" tab inside the device's pages in iTunes, you'll see CineXPlayer listed below, in "File Sharing". Select CineXPlayer and drag movies to the "Documents" pane.
Ta da!
In iTunes, on your first machine, you will have to go to File|Library|Export Library.
This will generate your Library.xml file.
If you take a look in it, you will see for each file all the fields you will find in iTunes (location on HDD, play count, rating, etc...).
Now, on your new machine, after having installed iTunes, you have to go to File|Library|Import Playlists (not obvious at first as I was looking at an Import Library menu but it doesn't exist) and select the xml file you exported on your first machine.
If you try, as I did first, to edit the xml file and overwrite the newly created one, when launching iTunes, it will delete it and create again an empty new one. You have to go through this Export/Import process (which is quite quick).
PS: you may have to edit the xml file anyway before importing, if the paths to the music files changed from your initial machine. For example, I upgraded from WinXP to Win7. As the user folder path changed, I then had to edit the paths c:\users and documents\myuser\My Documents\My music to c:\users\myuser\Music, or something like that, I don't remember exactly.
PPS: Always keep your exported xml file untouched somewhere until you have everything OK on your new machine...
Best Answer
Apple has a support document for this: iTunes: How to move your music to a new computer. It also covers things like de-authorizing your old computer from the iTunes Store etc.