Excluding bitcoin and simple clones, here's my pick of the most promising systems with a quick description taken from their websites.

BitConnect - Proof of Work/Proof of Stake

BitConnect Coin is an open source, peer-to-peer, community driven decentralized cryptocurrency that allow people to store and invest their wealth in a non-government controlled currency, and even earn a substantial interest on investment. This means anyone holding BitConnect Coin in their wallet will receive interest on their balance in return for helping maintain security of the network.

Stellar - Stellar Consensus Protocol

An open-source codebase for a decentralized worldwide payment protocol. Stellar uses the Stellar Consensus Protocol (SCP), a construction for federated Byzantine agreement (FBA). SCP provides a way to reach consensus without relying on a closed system to accurately record financial transactions. SCP is the first provably safe consensus mechanism that simultaneously enjoys four key properties: decentralized control, low latency, flexible trust, and asymptotic security.

BitShares - Delegated Proof of Stake

BitShares provides a high-performance decentralized exchange, with all the features you would expect in a trading platform plus a lot more.

Waves - Proof of Stake

Waves is a so-called decentralized, financial trading platform written in Scala and built on its own blockchain with custom tokens being its main feature. Custom tokens, or 'Custom Application Tokens', short CATs, allow for a wide range of uses. They enable decentralized crowdfunding as well as transferring, trading and storing of fiat and digital currencies.

Ethereum - Proof of Work/Proof of Stake

Ethereum is a decentralized platform that runs smart contracts: applications that run exactly as programmed without any possibility of downtime, censorship, fraud or third party interference.

NEM - Proof of Importance

NEM is a blockchain project which caters to much more than only handling it's native currency tokens "XEM". Above that, and more importantly, NEM is a peer to peer platform and it provides services like payments, messaging, asset making, and naming system.

IOTA - Tangle

IOTA is a revolutionary new transactional settlement and data transfer layer for the Internet of Things. It’s based on a new distributed ledger, the Tangle, which overcomes the inefficiencies of current Blockchain designs and introduces a new way of reaching consensus in a decentralized peer-to-peer system. For the first time ever, through IOTA people can transfer money without any fees. This means that even infinitesimally small nanopayments can be made through IOTA. IOTA is the missing puzzle piece for the Machine Economy to fully emerge and reach its desired potential. We envision IOTA to be the public, permissionless backbone for the Internet of Things that enables true interoperability between all devices.

Stratis - Proof of Stake

Stratis offer simple and affordable end-to-end solutions for development, testing and deployment of native C# blockchain applications on the .Net framework. Our platform consists a number of features including a cloud based service and a Blockchain development API.

Sia - Proof of Work

Sia leverages the capacity of blockchain technology to enable distributed networks to reach consensus in a secure and trustless way. Cryptographically secured smart contracts ensure the encryption and transfer of data with no possibility for a third party to interfere in any way. Sia is a new approach to cloud storage platforms. Instead of all datacenters being owned and operated by a single company, Sia opens the floodgates and allows anyone to make money by renting out their hard drive. Data integrity is protected using redundancy and cryptography.

Lisk - Delegated Proof of Stake

Lisk is a cryptocurrency that offers a next generation platform that allows for the development and distribution of JavaScript based blockchain applications. Lisk provides an easy to use interface and access full featured ecosystem. Through Lisk, developers can build, publish, distribute, and monetize their applications within a cryptocurrency powered system that allows for the use of customized blockchains, smart contracts, cloud storage, and computing nodes.

Ardor - Proof of Stake

Ardor is a blockchain-as-a-service platform that will allow people to utilize the blockchain technology of Nxt through the use of child chains. Since all processing will be done on the Ardor main chain, child chain creators won’t need to worry about common issues when creating a blockchain as well as securing it with enough nodes. Child chains will be able to utilize features currently seen in Nxt such as decentralized phasing, voting, and trading, as well as be able to interact with other child chains on the platform, including IGNIS, the first child chain to be launched.

The One To Watch

Out of all the systems I've looked at, IOTA seems by far the most revolutionary. Whereas other systems are merely evolutions of blockchain technology, IOTA brings an alternative to the blockchain which seems every bit as revolutionary as the bitcoin blockchain itself was. The next generation cryptocurrencies wont be using blockchains - they'll be using tangles.