Where does the litecoin wallet store coins? I recently installed the official LiteCoin wallet on Ubuntu. I accidentally deleted it about 80% of the way through the synch, and reinstalled it, expecting it to resynch. It resumed. My address didn't change either.

So it seems that the wallet data is stored somewhere in the system. Is this safe? I reasonably expect my system to eventually implode, so I will need to backup/export my data somehow.

Where is the data stored, and how do I back it up?
On Linux, the default data directory is ~/.litecoin/. This is where the wallet, blockchain, configuration, etc. files are stored.

You can backup your wallet from File > Backup Wallet. This is the part that contains your private keys. See the pic:



You should encrypt with a secure passphrase (in Settings > Encrypt Wallet) before exporting your wallet. If you don't, the private keys in your backup will be unencrypted. As long as your wallet has been encrypted, your backup will be encrypted and you can safely* put it on Dropbox, Google Drive, email it to family/friends, etc. for safe-keeping.

*As safe as your passphrase is, so make it very high quality.