Is it possible to sync my own video with Google Play Video (like in Google Play Music)?
I know that it's not possible on Google Books, I am wondering how about videos.
What will be a good alternative for syncing videos?
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Right now it is not possible to sync through Play Video, however, you may soon be able to purchase movies from the market and have them stay in the cloud until needed.
You could try alternatives such as Box, or Dropbox, (there are many competitors in this file-locker space), they allows you to sync nearly anything across devices.
Google Video, at least on my Xoom, will pick up movies out of any folder without the .nomedia file in it.
(edited to remove falsehood of no Google Services allowing syncing :) )
If you use Google+, you could install the Google+ app which can auto-upload videos and photos from your phone to your G+ account.
These photos and videos can also be accessed online via Picasa Web Albums which point to the same place as your Google+ photo albums. On the phone these become visible in the built-in Gallery app, if you enable the
Sync Google Photos and
Sync Google+ options on your account via
Settings -> Accounts & sync -> <your Google account>. On the desktop you can use Google's own Picasa application to organize and sync your photos/videos between your PC and your Google account.