If a new currency was developed that solved some of the big problems that Bitcoin has[2], possibly by working in a fundamentally different way, I can see that currency becoming the dominant digital currency.
1. https://en.bitcoin.it/wiki/List_of_alternative_cryptocurrenc...
2. People disagree on this, but I would list things including its deflationary nature and its fragility (human error can cause vast losses in a way that traditional banking prevents). On the other hand, a currency that really was anonymous would serve a purpose too.
In (not only) that sense, Bitcoins have more in common with hard dollar bills than with bank funds. If you burn your dollar bills or lose them in some other way, they are gone forever. Similarly, it is not possible to duplicate a dollar bill. In this regard, Bitcoin is even more secure since forgery is not possible either.
As epaga points out, if you lose access to your wallet (forget password, hardware failure without backups, somebody dies without leaving the password to their heirs) there is no way to retrieve that money.
Secondly, if a transaction is made to a valid-according-to-the-protocol address that nobody owns, that money is lost with no possibility of getting it back.
You could argue that these are problems that can be solved with more technology on top of Bitcoin, so you could have Bitcoin banks that:
1) Guarantee that your wallet is stored securely. The idea is that you need to trust that the bank is better at not doing stupid things than you.
2) Control access to it. Like modern banks, you would need to trust these banks, for they would have access to your wallets.
3) Make sure that payments are going to the right place. To make a payment, the bank that controls the wallet that the payment is being made to could be required to notify via another protocol that the address is real and belongs to a certain person/organisation. If this was widely used (so that payments to raw addresses was considered dangerous), it would also prevent a hacker from breaking into, say, EFF's Twitter account and tweeting "we're now accepting donations on this address...".
As for a big impact on the value of bitcoin, I don't think so. Bitcoin has the networking effects for now, many people are working on accepting them. It may be that the additional cost of accepting, for example LTC is lower when already accepting BTC, but BTC has a large first mover advantage.
All these make it seem like a better alternative for micro-transactions in the end.
I'm just wondering in terms of psychology, what impact it has to write in ever decreasing denominations? Pricing something as 0.000232 BTC is much more difficult to read and understand. So, if there are more coins in circulation, this would hopefully not happen until much later. It will inevitable happen (if it is also a success). But just for adoption and ease of use in the short and medium term it will be easier to read.
You can check out btc-e.com and see the absolutely massive price spike of litecoin. It went from .80c two weeks ago to trading at $4 consistently over the last week.