An introduction
Bitcoin was the first cryptocurrency released to the public in January 2009. Since then, there have been thousands of others modeled after it, with varying degrees of similarity to the original concept.
Even early on, the types of ‘altcoins’ (alternate cryptocurrencies) varied significantly from one another. Broadly, the following categories emerged:
Cryptocurrencies that changed a few technical or economic parameters from bitcoin. Examples include litecoin, which changed the mining algorithm used, total supply, and block times.
Cryptocurrencies that were built from a different codebase altogether, with some specialized purpose. Examples include NXT, a proof-of-stake coin with functionality that differed from the bitcoin blockchain.
Meta-protocols on top of bitcoin. Examples include Mastercoin and Counterparty, which extend the use cases of bitcoin by building a layer on top of it, yet still using bitcoin as the underlying protocol.
Alongside the initial developments, a fourth type of crypto token also emerged. This differed from the previous cryptocurrency tokens in that the primary application is not for use as a currency. Instead, these tokens were specific to an application, and required to the use of that application.
The value of these crypto tokens came, not so much for their use in the exchange of goods and services, but rather the use of the underlying service that required these tokens to operate. These have been called everything from 'appcoins' to 'protocol tokens'. It is important to note that the economic and financial principles underlying these crypto tokens can be vastly different.
Several examples of these application-specific crypto tokens emerged early on:
MaidSafeCoin, which is convertible to SafeCoin, is needed to use the SAFE network.
BitShares has its own token that is needed to create market-backed collateralized assets and trade those on the blockchain.
Storj has its own native crypto token for the application of decentralized storage.
Ethereum, the second largest crypto token after bitcoin, was founded on the same principle, allowing anyone to create arbitrarily complex smart contracts enforced and executed by the blockchain. The native crypto token, ether, is used to reward those who run the network's computations.
The flexibility with which contracts could be programmed on ethereum gave rise to many projects listing their own application-specific crypto tokens on the platform. Just in the last year, we have seen all sorts of applications, from digital management rights to in-game currencies, being listed as crypto tokens on ethereum. Some alternative blockchains, like Waves, were built specifically to help new projects issue and manage these crypto tokens.
A Framework for Valuing Crypto Tokens 
