Offline Bitcoin Wallet I would like to have bitcoin and store them as safely as possible. I want bitcoin data to be stored on my disk -- I don't want to some online service to manage my wallet. I also would like to have ability to easily backup wallet data so if my disk fails I can then recreate my wallet from backup.

Nice thing is to have ability to transfer wallet from one program to another so if some program ceased to be developed I can import my private/public keys to another program.

Can you recommend any application like that?
The only thing you need to spend bitcoins is a Private Key, I recommend that you create a Private Key beeing offline, then import it to Bitcoin Core wallet or Electrum Bitcoin wallet (if you don't want to download the complete blockchain) these are the most secure protocols.

First you need to create a Private Key, it consist on a 32 byte array on HEX format(64 characters), you can use SHA256, for example: ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb

Its highly recommended that you make this process offline and the input of the SHA256 should be as random as you can.

Then convert it to Wallet Import Format (WIF) following this guide: https://allprivatekeys.com/what-is-wif.

Then import WIF to the wallet:

Bitcoin Core: https://en.bitcoin.it/wiki/Help:How_to_import_private_keys_in_Bitcoin_Core_0.7%2B

Electrum: https://bitcoinelectrum.com/importing-your-private-keys-into-electrum/