Is there some standard term to describe all Bitcoin-like internet currencies, like Solidcoin, Namecoin and so forth? Like "currency" is to dollar, euro, yen, etc?
distributed digital currency, or distributed digital crypto-currency. the "distributed" bit is a key issue - anyone can make a centralized digital currency, even with crypto thrown in.
It's called crypto-currency, Wikipedia article.
I use "chain currencies". There are precedents for crypto currencies. OT currencies are also crypto-currencies. Ripple IOUs use cryptoGraphy in the distributed protocol too. The uniqueness is definitely in the block chain. I often refer to them as just "coins" since most of them are called SomethingCoin.
I think crypto-currency is the good term.
But personnally I tend to use digital currency because crypto can scare some users.