I don't understand why people need to create alternatives to Bitcoin such as litecoin. Why were these created? What's the point? You can't answer those questions using the same arguments for why Bitcoin was created.
In addition to Lohoris's answer, the reason that litecoin was created was to be as resistant to custom built hardware just for mining the coins, it uses scrypt as its cryptographic function. Scrypt was specifically designed to make it as expensive as possible to create hardware that is specifically good at doing that hash function. I personally like this because I do not like the idea of buying hardware that can only do SHA-256 to mine cryptocoins.
There is also ppcoin (pdf warning) which is aimed at not relying on constantly using electricity to keep the network secure. In this way it is very distinct from bitcoin.
The reason many people are trying different types of currencies is that Bitcoin not just a generic coin. It has certain properties built in such as only 21,000,000 ever existing, the 10 minutes taken to confirm a transaction, halving the production rate and importantly the initial distribution been given to miners. Many people like the concept of Bitcoin but disagree with one or more of the above properties and the only way to get around those properties is to create a new currency (or at least fork Bitcoin).
Namecoin had a reason to be created: it is not intended as a currency, it is intended as an alternative DNS system. Here you find the explaination about why they had to create a separate currency instead of "just using Bitcoin's blockchain".
It failed due to their foolish choice to have the domains be basically free.
Nextcoin (NXT) uses a proof-of-stake instead of the Bitcoin's proof-of-work. This is much more eco-friendly, so that's definitely a good reason to create it. It also has many other features, being a completely different codebase.
As @jtimon correctly points out, some coins (such as Freicoin) were created to experiment with different economic models, so, despite having extremely small chances of success, at least they were/are worthy experiments.
All of the other Bitcoin-like currencies are either scams (Solidcoin) or the product of kids who desperately wanted to "play miner" and were disappointed they couldn't do it anymore with their hardware: they created special coins with the goal of being optimised for their current hardware, instead of the goal of being as secure as possible.
Not only this is (obviously) a very poor design choice, but it was also doomed to fail in the long run: if those currencies were to have success (not that they had any real chance), custom hardware would have been built anyway, spawning in future more kids who weren't able to "play miner" with that currency either.
Sorry for being harsh but speaking out the truth is what is needed in such a question.
Everyone doesn't have to accept the same principle (philosophies) as of Bitcoin. Alternate coins (or even, Ripple) in a more simplified way, just Bitcoin with various parameters (philosophies) adjusted. like it or not, bitcoin does reward early-adopters unfairly(?). may be Bitcoin did that for survival / evolution purpose. After all it is open market, and always there is an opportunity for new financial services.
For example, when a government wants to adopt it then it could simply start bitcoin-like public ledger, sign and log all (?) the transactions, take mining out of equation, etc. there are various parameters, so many options and preferences vary.
Bitcoin's very different things to different people, and obviously can't be everything to everyone. A lot of people really like a subset of its properties whilst disliking others. Some aspects of bitcoin are modifiable by comunity vote, some others not, and implementing yet others may require too much changes to the core code.
By allowing forks to be created, different ideas of what a crypto-currency can and maybe should be are competing directly against one another, in a Darwinian-like evolution.
Litecoin, for instance, tried to address 3 perceived problems with Bitcoin (others don't perceive them as problems or may even regard them as features): transactions taking too much to confirm, a "small" ceiling as to the max. number of currency to be mined, and a hash function that gives a very unfair advantage to users with GPUs and ASICs - theoretically this last one could mean mining will end-up, in the long term, concentrated in very few hands, besides making it potentially easy for governments with deep-pockets to mount a 51% attack by deploying large clusters of ASICs.
By producing blocks every 2-3 minutes, having a top of 80 million litecoins and using a CPU-friendly (and GPU-unfriendly!) algorithm, these perceived problems are avoided.
PPCoin addresses the perceived high-electricity consumption of the bitcoin network by having a radically new way to distribute newly created coins: appart from "classic mining", the amount of coins you already have serves as a "proof-of-stake" which is rewarded as well with even more coins, randomly. This way, new coins are produced without the need of lots of miners, potentially reducing the net electric consumption of the PPCoin network by 1 or 2 orders of magnitude as compared to Bitcoin. Since this proof-of-stake would encourage hoarding (and possibly high deflation!), a new built-in, inflation-like parameter is introduced so that each transaction destroys a number of your coins - supposedly this compensates the former effect.
And finally Freicoin is an attempt to apply the ideas of Austrian-Argentine economist Silvio Gessell to a crypto-currency. Here, your coins are slowly "eroded" in value by a pre-fixed percentage every year. This has a number of very interesting economic effects: Disencourages hoarding, encourages fast circulation of coins, interest rates drop to near zero (since banks would lose money by storing it idly in their valves, they need to invest it as fast as possible), inflation gets stopped in its tracks(since instead of prices going up, money's value goes down, so to speak), etc.
I'm sure there's space in the market of ideas for even more different approaches than vanilla Bitcoin, or combining 2 or more of them (Novacoin, for instance, basically takes PPcoin and mixes it with Litecoin). I can think of: unlimited max. number of coins, somehow increasing the amount of nodes controlled to mount a fatal attack (so instead of 51% you'd need 75% or the like), disencouraging miners to produce empty blocks, encouraging them to pick up transactions for small amounts, or rather highly discorage these transactions...
Let one hundred flowers blossom!!!
Bitcoin has certain properties that could be replaced with some other. Most altcoins to just that. Popular properties that altcoins change are:
- replace PoW with something else
Some altcoins do not use a PoW mechanism or use a hybrid mechanism. PeerCoin (originally named PPCoin) was the first altcoin to use the Proof-of-Stake mechanism, which basically requires miners to hold a certain amount of currency in order to mine new. PeerCoin uses a hybrid of PoS and PoW. Nxt is an altcoin that uses pure PoS.
- the PoW algorithm
Bitcoin uses SHA-256, which is a hash algorithms that almost entirely requires CPU cycles to calculate. This means that it is easy to create custom hardware to perform this calculations. There are many altcoins that use Scrypt as the PoW algorithm. Scrypt is more memory-intensive and therefore harder to implement in custom hardware. The first altcoin to implement Scrypt is Litecoin. Primecoin requires miners to calculate large prime numbers as a PoW mechanism.
- the total amount of coins that can be mined
- the rate at which new blocks are created
Bitcoin blocks are mined at an average rate of one block every 10 minutes. Many merchants require that a transaction has been confirmed by several blocks before they accept it. With a confirmation time of 10 minutes (in fact, the recommended amount of confirmations to wait for is 6) can be quite cumbersome in certain use cases. Litecoin has a confirmation time of 2.5 minutes.
- the time it takes before the maximum amount of coins is created
Block rewards usually have a halving time. Every halving time the block reward halves until it is too low to represent using the maximum precision and it becomes zero. With Bitcoin it will take until 2140 until the block reward becomes zero. Some coins shorten this period. Sometimes they shorten it so much that the creator (who mines first, of course) is accused of pre-mining because he can mine very fast and easy in the beginning of the existence of the coin.
Bitcoin is open source and one can add new features. Some do this by contributing to the Bitcoin client, some by creating alternate clients with different features while still operating on the same block chain and protocol.
However one cannot add apposing features such as apposing economic theories (an inflationary currency vs a deflationary currency) or apposing security incentives (stake holders vs resource holders), regardless of the accessibility of the source code. Also, Bitcoin has an additional hurdle to contribution above the bar of commit rights on the source code; the entire (read 50+%) community of users must agree with your alterations and adopt your changes if they alter the protocol.
For this reason other cryptocurrencies are being created to provide alternative technical or economic solutions. One of these my prove to be a better solution, or we may end up with a selection of different digital currency 'instruments' with usefully different properties like stocks vs options vs bonds.
Although some alternatives have been developed to make smaller changes to perceived technical limitations of Bitcoin such as number of total coins, distribution rate, confirmation rate, etc. these are probably only of academic or research interest. If any of these types of changes proved to be useful they could easily be incorporated into the Bitcoin protocol itself rendering the alternate superfluous.