You could easily create a bitcoin2, bitcoin3, ... you could create an infinite number of bitcoin currencies having different parametric spaces. These would live in separate mathematical spaces however, so you wouldn't for example be able to create bitcoins in bitcoin2 that affect bitcoins in the original bitcoin: it would be a completely separate system.

But we don't need to be so theoretical about this; there are many alternative digital currencies already in existence:

https://en.bitcoin.it/wiki/Category:Digital_currencies

I would also add other forms of popular credit such as paypal credit, and the new Amazon coin that is coming out to that list.

These can co-exist and there is no problem in this.

I think as a challenger of bitcoin however, it would be difficult, as bitcoin is the most established and most popular digital currency so far. People tend to invest in what is already the most popular, so you get a compounding effect due to this. But this isn't to say that something like something like Amazon coin couldn't eclipse bitcoin for popular use.

Note that these currencies also vary in anonymity and liquidity, which will also affect how popular they become.

But I think in summary I have to say that nobody can predict the future for this kind of thing, so we'll just have to wait and see.

You could read what Rothbard has to say about free money in a free market. I personnally think everbybody should be allowed to make money. If the market accepts it, it is real money. The more diverse the monetary ecosystem, the more stable it probably is also.

http://mises.org/Books/mysteryofbanking.pdf

Just a couple of days ago I made a blog post, and about half of it was dealing with this question: http://www.economicsofbitcoin.com/2013/03/the-classification-future-of-bitcoin.html

EDIT: basically, since a new network is not compatible (just see the recent block size hardfork debate) it is a question of network effect. If the network effect is strong, competitors will have it more difficult to take away market share from bitcoin, and have to present a compelling reason to switch. Economists tend towards the position that money has a strong network effect. In a cryptocurrency world, a competitor would have to spend a lot of money on the infrastructure, such as software libraries, documentation, PR, merchant integration, and provide liquidity on the exchanges. Probably also on lawyers.

An analogy that I often use are languages or the IP (protocol). It also is easy to create a new incompatible standard for these, just the idea that one day you wake up suddenly everyone uses something else is implausible. IPv6 has existed for 20 years now, and still hasn't replaced IPv4, because there is so much infrastructure that's not compatible and people don't want to spend money on replacing them. That's not to say that a switch cannot occur, just that it takes time and resources. I expect that eventually, IPv6 (or its successor) will replace IPv4. The IPv6 share of network traffic has been rising.

Eventually, Bitcoin may also be replaced by some other alternative that people find better. So far, that doesn't seem to be happening. The only alternative that seems to have a shot at all so far seems to be Ethereum.

For a reference, look at https://coinmarketcap.com, where hundreds of competitors to Bitcoin fail to gain non-negigible market share.