Decred (DCR) is a decentralized currency with an emphasis on community based governance. Decred is led by several early adopters of Bitcoin and is designed to implement many of the goals of early Bitcoin idealists. Decred is highly focused on community contribution and governance. Users that contribute to the community can receive compensation for their work and anybody can submit a proposal ti make an improvement to the platform.
Decred has a hybrid Proof-of-Activity (PAC) consensus algorithm that combines the mining of Proof-of-Work (PoW) with the stake verifying model of Proof-of-Stake (PoS). It's designed to incentivize the community to participate and to reward both miners and stake verifiers. When DCR is mined, PoW miners receives 60% of the coins, PoS voters receive 30%, and 10% goes towards the development of the Decred platform.

.

Primecoin is a cryptocurrency based on finding prime numbers. Identifying prime numbers plays a central role in cryptography. Primecoin's unique Proof-of-Work (PoW) consensus mechanism is able to increase transaction speeds and improve energy efficiency.
The network searches for special prime number chains known as Cunningham chains and bi-twin chains, which are of interest in mathematical research.

FREE Coin is an Ethereum-based token with a focus on being inclusive and encouraging cryptocurrency adoption. Their goal is for the token's price to increase in value, until its price is close to the USD. FREE Coin's site does not provide any details about their development plan or what specific advantages their network will provide.