The aim of the currencies below is to make it impossible for an investigator to analyze a public ledger, known as block chain in Bitcoin, and to hide the identities of those making and receiving payments. Other advantages are that the money can not be seized and transaction fees are very low or non existent.
WARNING! The world of cryptocurrencies contain elaborate scams, pump and dump and pyramid schemes. I am not endorsing any of the currencies below, it is your duty to double check claims about anonymity and trust.
Dash (DASH): One of the most popular, Digital Cash is a Bitcoin based electronic currency focused in privacy. The wallet contains a coin mixer, you have the choice to make your financial operations public or anonymous, using a decentralized network of servers called masternodes that anonymize the transaction, the level of anonymity can be configured to in between 2 or 8 node hops. Digital Cash coins can be earned if you help the network running a masternode but this is not necessary.
CloakCoin (CLOAK): Every CloakCoin user becomes part of the network which increases anonymity, in exchange for keeping your wallet open and helping others be anonymous, you earn interest on the CloakCoins you hold. A built in decentralized market called OneMarket can be used to spend your currency anonymously, anybody can advertise and buy services or goods in OneMarket, or you can exchange your coins in CloackTrade.
ShadowCash (SDC): Decentralised cryptocurrency with the choice of making public or private anonymous payments. When you open your wallet it will help run the peer to peer network and you will be compensated with electronic cash. ShadowCash comes with an embedded private messenger that encrypts communications and allows you to talk with other users on the network.
LEOCoin (LEO): The Learning Enterprise Organisation coin has a focus on being user friendly, it has a decentralized peer to peer payment system with proof of work and proof of stake validation. The public ledger is encrypted. An article in Coindesk has scam accusations against the developers of this currency, I would be very careful with it, the accusations are somehow substantiated with real facts.
AnonCoin (ANC): Anonymous cryptocurrency with native support for the I2P network, it can also be used over Tor, AnonCoin will not only decentralized operations but it also anonymizes computer IPs when you connect to a client. This currency has been around for two years and development is very active, with good documentation, a Wiki and discussion forum, it can be traded in various exchanges.
Monero (XMR): Open source untraceable currency using peer to peer transactions and a distributed public ledger, receipts and money transfers remain private by default. Ring signatures add a degree of ambiguity to make it harder to link a transaction with an individual computer. This currency can be integrated in the I2P anonymous network and you can run a full node if you want to, another choice is to use a web based Monero account.
BitcoinDark (BTCD): It has a very novel unproven approach to currency anonymity, BitcoinDark uses what they call Teleport to clone and exchange currency denominations out of the block chain. A hard to understand technology, first generation cryptocurrency. BitcoinDark is part of SuperNET, a decentralized currency exchange that makes it very difficult to steal digital currency by storing it in multiple nodes.