It's not common yet, but I have in fact saved money by buying with bitcoins, because the merchant passed on some of the savings.
>Isn't it just easier to buy things with Dollars?
Sure, if you're allowed to, and you have that preference, why not? Bitcoin can facilitate the circumvention of censorship (a la Wikileaks). And once you have bitcoins, sending them is faster than paying with a credit card online.
>Doesn't it require increasingly more capital to mine coins and to maintain the ledger?
Yes, if you ignore hardware advances. It might even be true if you don't ignore that.
>What happens when the value of a coin is less than the mining costs or ledger maintenance?
There are transaction fees that go to the block miner.
>Or, does the coin just keep continuing to increase in value?
Hopefully not too quickly!
>what's to stop people from just using another crypto-currency?
Network effects. People do use other crypto-currencies. Just not as much. For now.
>And, what is the 'value' of a coin? The article implies that the value is created by the users' trust in the value. But, is that how currencies generally work? I had assumed that currencies either have tangible value, like precious metals, or that they are abstract derivatives of another's debt (government or people).
Ah, yes. This is classic. The orthodox economists might tell you that Bitcoin shouldn't have any value at all. Yet, I can sell 1 BTC and pay for months of gas. I'd rather have a running car than an economist's opinion.
There are historical examples of currency which was neither a debt derivative nor an intrinsically useful object being used as currency.
Ultimately, anything sellable is "worth" what other people will pay for it. Bitcoin provides a means of transferring information in a cryptographically signed manner. We happen to use that fact to transfer information about value. Other people are willing to buy bitcoins. The price is capped by the fact that there is a finite number of bitcoins and a finite number of people. Beyond that, it's pretty much new ground we're breaking here.
Bitcoin is not perfect. I don't know the future. But if you have other questions, I'm happy to answer them from the perspective of a bitcoin holder.