Online Bitcoin Wallets
Blockchain.info – Provides an encrypted online wallet that can be backed up on paper and accessed over Tor, with Shared Coin mixing service built in.
Desktop Bitcoin Wallets
Armory – State of the art bitcoin wallet that is easy to use and provides cold storage. The latest Armory version will work on systems with only 1-2 GB RAM. No other bitcoin wallet provides the ultimate security and ease of use of Armory.
Electrum – Lightweight bitcoin wallet that is also available in a portable version you can carry on a USB drive. If you require a portable wallet that also offers cold storage consider Electrum.
Hive – New desktop bitcoin wallet for Mac OSX.
Armory and Electrum are the only desktop wallets that are deterministic (only need to be backed up once) and both can be connected over Tor. Armory is very user friendly and suitable for anyone … even someone brand new to bitcoin … while Electrum is best suited for advanced users.
Remember to connect your bitcoin wallet over Tor or a good VPN like Private Internet Access unless you want your true IP to be linked to your bitcoin transactions.
Mobile Bitcoin Wallets
Blockchain for Android – recommended for ease of use and advanced features like built in bitcoin mixing and connection over Tor using the Orbot app.
Electrum for Android – at present Electrum is not available native as an app but can still be installed on an Android phone by following directions here.
Coinpunk for iPhone – The easy mobile wallet for iPhone. There are no bitcoin wallets for iPhone in the App Store due to official Apple policy. If you have a jailbroken iPhone the Blockchain.info wallet for iPhone can also be found here.