How can I copy videos and photos to my iPad without syncing?

You can use something like iPhone Explorer to drag and drop them into the /User/Media/DCIM/100Apple (last one may be different) directory. I know it works with pictures, but I haven't had a chance to test with video. But I don't see why it wouldn't work once the database is updated.

If you're jailbroken and transfer a video, that the phone can play, with iPhone Explorer (works on Mac and Windows for iPad and iPod too) or through SSH (with the OpenSSH package from Cydia), iFile can add it to the camera roll (same with pictures, and it doesn't matter where they are if you use the SSH and iFile method). Not exactly drag and drop but you don't have to go through iTunes. iPhone Explorer does not require the iDevice to be jailbroken.

Also if you got the VLC Player app before Apple pulled it you can drag and drop almost any video type into the app via the "File Sharing" box in iTunes in the App tab. (If the phone is jailbroken you can still get the VLC player from Cydia)

In iTunes, go to the iPad’s (or iPod’s) summary screen. Check the “Manually manage videos” box, and click the “Apply” button. You can then drag videos from your desktop to the iPad without having to sync.

DropBox on your main machine would allow you to add both files to your iPad without sync. The iPad should automatically play files it recognizes in the proper application when it sees them there. Dropbox provides 2GB of storage for free so going above that will require payment.

Edit You can 'star' files if you want them downloaded to the device so you'll have them even if offline.